%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 19.68s 3.08s
% Output : CNFRefutation 19.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:53:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.68/3.08 % SZS status Theorem for theBenchmark.p
% 19.68/3.08 % SZS output start CNFRefutation for theBenchmark.p
% 19.68/3.08 fof(path_properties, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X0,X1,X2) => (vertex(X0) & (vertex(X1) & ? [X3] : ((edge(X3) & (X0 = 'tail$uof'(X3) & ~(((X1 = 'head$uof'(X3) & X2 = 'path$ucons'(X3,empty)) <=> ? [X4] : ((path('head$uof'(X3),X1,X4) & X2 = 'path$ucons'(X3,X4))))))))))))).
% 19.68/3.08 fof(on_path_properties, axiom, ! [X0] : ! [X1] : ! [X2] : ! [X3] : (((path(X0,X1,X2) & 'on$upath'(X3,X2)) => (edge(X3) & ('in$upath'('head$uof'(X3),X2) & 'in$upath'('tail$uof'(X3),X2)))))).
% 19.68/3.08 fof(precedes_properties, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X1,X2,X0) => ! [X3] : ! [X4] : ((precedes(X3,X4,X0) => ('on$upath'(X3,X0) & ('on$upath'(X4,X0) & ~((sequential(X3,X4) <=> ? [X5] : ((sequential(X3,X5) & precedes(X5,X4,X0)))))))))))).
% 19.68/3.08 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$uof'(X3))))))))).
% 19.68/3.08 fof(shortest_path_properties, axiom, ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & precedes(X2,X3,X4)) => (~? [X5] : (('tail$uof'(X5) = 'tail$uof'(X2) & 'head$uof'(X5) = 'head$uof'(X3))) & ~precedes(X3,X2,X4))))).
% 19.68/3.08 fof(vertices_and_edges, conjecture, ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & precedes(X2,X3,X4)) => (vertex(X0) & (vertex(X1) & (X0 != X1 & (edge(X2) & (edge(X3) & (X2 != X3 & path(X0,X1,X4)))))))))).
% 19.68/3.08 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & precedes(X2,X3,X4)) => (vertex(X0) & (vertex(X1) & (X0 != X1 & (edge(X2) & (edge(X3) & (X2 != X3 & path(X0,X1,X4))))))))), inference(negate_conjecture, [status(cth)], [vertices_and_edges])).
% 19.68/3.08 cnf(c31, plain, ~path(X0,X1,X2) | X3(X2,X0,X1), inference(clausification, [status(esa)], [path_properties])).
% 19.68/3.08 cnf(c35, plain, ~X0(X1,X2,X3) | vertex(X2), inference(clausification, [status(esa)], [path_properties])).
% 19.68/3.08 cnf(c36, plain, ~X0(X1,X2,X3) | vertex(X3), inference(clausification, [status(esa)], [path_properties])).
% 19.68/3.08 cnf(c45, plain, ~path(X0,X1,X2) | ~'on$upath'(X3,X2) | edge(X3), inference(clausification, [status(esa)], [on_path_properties])).
% 19.68/3.08 cnf(c60, plain, ~path(X0,X1,X2) | ~precedes(X3,X4,X2) | X5(X3,X4,X2), inference(clausification, [status(esa)], [precedes_properties])).
% 19.68/3.08 cnf(c61, plain, ~X0(X1,X2,X3) | 'on$upath'(X1,X3), inference(clausification, [status(esa)], [precedes_properties])).
% 19.68/3.08 cnf(c62, plain, ~X0(X1,X2,X3) | 'on$upath'(X2,X3), inference(clausification, [status(esa)], [precedes_properties])).
% 19.68/3.08 cnf(c69, plain, ~'shortest$upath'(X0,X1,X2) | X3(X2,X0,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 19.68/3.08 cnf(c71, plain, ~X0(X1,X2,X3) | path(X2,X3,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 19.68/3.08 cnf(c72, plain, ~X0(X1,X2,X3) | X2 != X3, inference(clausification, [status(esa)], [shortest_path_defn])).
% 19.68/3.08 cnf(c77, plain, ~'shortest$upath'(X0,X1,X2) | ~precedes(X3,X4,X2) | ~precedes(X4,X3,X2), inference(clausification, [status(esa)], [shortest_path_properties])).
% 19.68/3.08 cnf(c78, plain, 'shortest$upath'(sK75,sK76,sK79), inference(clausification, [status(esa)], [negated_conjecture])).
% 19.68/3.08 cnf(c79, plain, precedes(sK77,sK78,sK79), inference(clausification, [status(esa)], [negated_conjecture])).
% 19.68/3.08 cnf(c80, plain, ~vertex(sK76) | ~edge(sK77) | sK77 = sK78 | sK75 = sK76 | ~vertex(sK75) | ~edge(sK78) | ~path(sK75,sK76,sK79), inference(clausification, [status(esa)], [negated_conjecture])).
% 19.68/3.08 cnf(d0, plain, 'Ts63'(sK79,sK75,sK76), inference(resolution, [status(thm)], [c69,c78])).
% 19.68/3.08 cnf(d1, plain, path(sK75,sK76,sK79), inference(resolution, [status(thm)], [c71,d0])).
% 19.68/3.08 cnf(d2, plain, sK75 = sK76 | sK77 = sK78 | ~edge(sK77) | ~edge(sK78) | ~vertex(sK75) | ~vertex(sK76), inference(resolution, [status(thm)], [d1,c80])).
% 19.68/3.08 cnf(d3, plain, 'Ts30'(sK79,sK75,sK76), inference(resolution, [status(thm)], [d1,c31])).
% 19.68/3.08 cnf(d4, plain, vertex(sK75), inference(resolution, [status(thm)], [d3,c35])).
% 19.68/3.08 cnf(d5, plain, sK75 = sK76 | sK77 = sK78 | ~edge(sK77) | ~edge(sK78) | ~vertex(sK76), inference(resolution, [status(thm)], [d4,d2])).
% 19.68/3.08 cnf(d6, plain, vertex(sK76), inference(resolution, [status(thm)], [d3,c36])).
% 19.68/3.08 cnf(d7, plain, sK75 = sK76 | sK77 = sK78 | ~edge(sK77) | ~edge(sK78), inference(resolution, [status(thm)], [d6,d5])).
% 19.68/3.08 cnf(d8, plain, edge(X0) | ~'on$upath'(X0,sK79), inference(resolution, [status(thm)], [c45,d1])).
% 19.68/3.08 cnf(d9, plain, ~path(X0,X1,sK79) | 'Ts55'(sK77,sK78,sK79), inference(resolution, [status(thm)], [c60,c79])).
% 19.68/3.08 cnf(d10, plain, 'Ts55'(sK77,sK78,sK79), inference(resolution, [status(thm)], [d9,d1])).
% 19.68/3.08 cnf(d11, plain, 'on$upath'(sK77,sK79), inference(resolution, [status(thm)], [d10,c61])).
% 19.68/3.08 cnf(d12, plain, edge(sK77), inference(resolution, [status(thm)], [d11,d8])).
% 19.68/3.08 cnf(d13, plain, sK75 = sK76 | sK77 = sK78 | ~edge(sK78), inference(resolution, [status(thm)], [d12,d7])).
% 19.68/3.08 cnf(d14, plain, 'on$upath'(sK78,sK79), inference(resolution, [status(thm)], [d10,c62])).
% 19.68/3.08 cnf(d15, plain, edge(sK78), inference(resolution, [status(thm)], [d14,d8])).
% 19.68/3.08 cnf(d16, plain, sK75 = sK76 | sK77 = sK78, inference(resolution, [status(thm)], [d15,d13])).
% 19.68/3.08 cnf(d17, plain, precedes(sK77,sK77,sK79) | sK75 = sK76, inference(superposition, [status(thm)], [d16,c79])).
% 19.68/3.08 cnf(d18, plain, ~precedes(X0,X1,sK79) | ~precedes(X1,X0,sK79), inference(resolution, [status(thm)], [c77,c78])).
% 19.68/3.08 cnf(d19, plain, ~precedes(sK78,sK77,sK79), inference(resolution, [status(thm)], [d18,c79])).
% 19.68/3.08 cnf(d20, plain, ~precedes(sK77,sK77,sK79) | sK75 = sK76, inference(superposition, [status(thm)], [d16,d19])).
% 19.68/3.08 cnf(d21, plain, sK75 = sK76 | sK75 = sK76, inference(resolution, [status(thm)], [d20,d17])).
% 19.68/3.08 cnf(d22, plain, 'Ts63'(sK79,sK75,sK75), inference(demodulation, [status(thm)], [d0,d21])).
% 19.68/3.08 cnf(d23, plain, ~'Ts63'(X0,X1,X1), inference(equality_resolution, [status(thm)], [c72])).
% 19.68/3.08 cnf(d24, plain, $false, inference(resolution, [status(thm)], [d23,d22])).
% 19.68/3.08 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------