%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA008+2 : 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 : n014.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 07:18:43 AM UTC 2026
% Result : Theorem 23.99s 3.62s
% Output : CNFRefutation 23.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 13:47:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.99/3.62 % SZS status Theorem for theBenchmark.p
% 23.99/3.62 % SZS output start CNFRefutation for theBenchmark.p
% 23.99/3.62 fof(triangle_defn, axiom, ! [X0] : ! [X1] : ! [X2] : ((triangle(X0,X1,X2) <=> (edge(X0) & (edge(X1) & (edge(X2) & (sequential(X0,X1) & (sequential(X1,X2) & sequential(X2,X0))))))))).
% 23.99/3.62 fof(back_edge, lemma, (complete => ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & precedes(X2,X3,X4)) => ? [X5] : ((edge(X5) & ('tail$uof'(X5) = 'head$uof'(X3) & 'head$uof'(X5) = 'tail$uof'(X2)))))))).
% 23.99/3.62 fof(no_loops, axiom, ! [X0] : ((edge(X0) => 'head$uof'(X0) != 'tail$uof'(X0)))).
% 23.99/3.62 fof(complete_properties, axiom, (complete => ! [X0] : ! [X1] : (((vertex(X0) & (vertex(X1) & X0 != X1)) => ? [X2] : ((edge(X2) & ~(((X0 = 'head$uof'(X2) & X1 = 'tail$uof'(X2)) <=> (X1 = 'head$uof'(X2) & X0 = 'tail$uof'(X2)))))))))).
% 23.99/3.62 fof(sequential_defn, axiom, ! [X0] : ! [X1] : ((sequential(X0,X1) <=> (edge(X0) & (edge(X1) & (X0 != X1 & 'head$uof'(X0) = 'tail$uof'(X1))))))).
% 23.99/3.62 fof(precedes_defn, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X1,X2,X0) => ! [X3] : ! [X4] : ((('on$upath'(X3,X0) & ('on$upath'(X4,X0) & (sequential(X3,X4) | ? [X5] : ((sequential(X3,X5) & precedes(X5,X4,X0)))))) => precedes(X3,X4,X0)))))).
% 23.99/3.62 fof(precedes_properties, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X1,X2,X0) => ! [X3] : ! [X4] : ((precedes(X3,X4,X0) => ('on$upath'(X3,X0) & ('on$upath'(X4,X0) & ~((sequential(X3,X4) <=> ? [X5] : ((sequential(X3,X5) & precedes(X5,X4,X0)))))))))))).
% 23.99/3.62 fof(shortest_path_defn, axiom, ! [X0] : ! [X1] : ! [X2] : (('shortest$upath'(X0,X1,X2) <=> (path(X0,X1,X2) & (X0 != X1 & ! [X3] : ((path(X0,X1,X3) => 'less$uor$uequal'('length$uof'(X2),'length$uof'(X3))))))))).
% 23.99/3.62 fof(sequential_is_triangle, conjecture, (complete => ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & (precedes(X2,X3,X4) & sequential(X2,X3))) => ? [X5] : triangle(X2,X3,X5))))).
% 23.99/3.62 fof(negated_conjecture, negated_conjecture, ~((complete => ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & (precedes(X2,X3,X4) & sequential(X2,X3))) => ? [X5] : triangle(X2,X3,X5))))), inference(negate_conjecture, [status(cth)], [sequential_is_triangle])).
% 23.99/3.62 cnf(c1, plain, triangle(X0,X1,X2) | ~X3(X0,X1,X2), inference(clausification, [status(esa)], [triangle_defn])).
% 23.99/3.62 cnf(c8, plain, ~sequential(X0,X1) | ~edge(X2) | ~sequential(X1,X2) | X3(X0,X1,X2) | ~edge(X0) | ~sequential(X2,X0) | ~edge(X1), inference(clausification, [status(esa)], [triangle_defn])).
% 23.99/3.62 cnf(c16, plain, ~complete | ~'shortest$upath'(X0,X1,X2) | ~precedes(X3,X4,X2) | edge(sK23(X3,X4)), inference(clausification, [status(esa)], [back_edge])).
% 23.99/3.62 cnf(c17, plain, ~complete | ~'shortest$upath'(X0,X1,X2) | ~precedes(X3,X4,X2) | 'tail$uof'(sK23(X3,X4)) = 'head$uof'(X4), inference(clausification, [status(esa)], [back_edge])).
% 23.99/3.62 cnf(c18, plain, ~complete | ~'shortest$upath'(X0,X1,X2) | ~precedes(X3,X4,X2) | 'head$uof'(sK23(X3,X4)) = 'tail$uof'(X3), inference(clausification, [status(esa)], [back_edge])).
% 23.99/3.62 cnf(c19, plain, ~edge(X0) | 'head$uof'(X0) != 'tail$uof'(X0), inference(clausification, [status(esa)], [no_loops])).
% 23.99/3.62 cnf(c29, plain, ~X0(X1,X2,X3) | X2 = 'head$uof'(X1), inference(clausification, [status(esa)], [complete_properties])).
% 23.99/3.62 cnf(c30, plain, ~X0(X1,X2,X3) | X3 = 'tail$uof'(X1), inference(clausification, [status(esa)], [complete_properties])).
% 23.99/3.62 cnf(c31, plain, X0(X1,X2,X3) | X2 != 'head$uof'(X1) | X3 != 'tail$uof'(X1), inference(clausification, [status(esa)], [complete_properties])).
% 23.99/3.62 cnf(c54, plain, ~sequential(X0,X1) | X2(X0,X1), inference(clausification, [status(esa)], [sequential_defn])).
% 23.99/3.62 cnf(c55, plain, sequential(X0,X1) | ~X2(X0,X1), inference(clausification, [status(esa)], [sequential_defn])).
% 23.99/3.62 cnf(c56, plain, ~X0(X1,X2) | edge(X1), inference(clausification, [status(esa)], [sequential_defn])).
% 23.99/3.62 cnf(c57, plain, ~X0(X1,X2) | edge(X2), inference(clausification, [status(esa)], [sequential_defn])).
% 23.99/3.62 cnf(c60, plain, X0(X1,X2) | X1 = X2 | 'head$uof'(X1) != 'tail$uof'(X2) | ~edge(X1) | ~edge(X2), inference(clausification, [status(esa)], [sequential_defn])).
% 23.99/3.62 cnf(c62, plain, ~sequential(X0,X1) | ~'on$upath'(X2,X3) | precedes(X0,X2,X3) | ~'on$upath'(X0,X3) | ~path(X4,X5,X3) | ~precedes(X1,X2,X3), inference(clausification, [status(esa)], [precedes_defn])).
% 23.99/3.62 cnf(c63, plain, ~path(X0,X1,X2) | ~precedes(X3,X4,X2) | X5(X3,X4,X2), inference(clausification, [status(esa)], [precedes_properties])).
% 23.99/3.62 cnf(c65, plain, ~X0(X1,X2,X3) | 'on$upath'(X2,X3), inference(clausification, [status(esa)], [precedes_properties])).
% 23.99/3.62 cnf(c69, plain, ~X0(X1,X2,X3) | ~sequential(X1,X4) | ~precedes(X4,X2,X3) | ~sequential(X1,X2), inference(clausification, [status(esa)], [precedes_properties])).
% 23.99/3.62 cnf(c72, plain, ~'shortest$upath'(X0,X1,X2) | X3(X2,X0,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 23.99/3.62 cnf(c74, plain, ~X0(X1,X2,X3) | path(X2,X3,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 23.99/3.62 cnf(c81, plain, complete, inference(clausification, [status(esa)], [negated_conjecture])).
% 23.99/3.62 cnf(c82, plain, 'shortest$upath'(sK81,sK82,sK85), inference(clausification, [status(esa)], [negated_conjecture])).
% 23.99/3.62 cnf(c83, plain, precedes(sK83,sK84,sK85), inference(clausification, [status(esa)], [negated_conjecture])).
% 23.99/3.62 cnf(c84, plain, sequential(sK83,sK84), inference(clausification, [status(esa)], [negated_conjecture])).
% 23.99/3.62 cnf(c85, plain, ~triangle(sK83,sK84,X0), inference(clausification, [status(esa)], [negated_conjecture])).
% 23.99/3.62 cnf(d0, plain, 'head$uof'(sK23(X0,X1)) = 'tail$uof'(X0) | ~precedes(X0,X1,X2) | ~'shortest$upath'(X3,X4,X2), inference(resolution, [status(thm)], [c81,c18])).
% 23.99/3.62 cnf(d1, plain, 'head$uof'(sK23(X0,X1)) = 'tail$uof'(X0) | ~precedes(X0,X1,sK85), inference(resolution, [status(thm)], [d0,c82])).
% 23.99/3.62 cnf(d2, plain, 'head$uof'(sK23(sK83,sK84)) = 'tail$uof'(sK83), inference(resolution, [status(thm)], [d1,c83])).
% 23.99/3.62 cnf(d3, plain, 'tail$uof'(sK23(X0,X1)) = 'head$uof'(X1) | ~precedes(X0,X1,X2) | ~'shortest$upath'(X3,X4,X2), inference(resolution, [status(thm)], [c81,c17])).
% 23.99/3.62 cnf(d4, plain, 'tail$uof'(sK23(X0,X1)) = 'head$uof'(X1) | ~precedes(X0,X1,sK85), inference(resolution, [status(thm)], [d3,c82])).
% 23.99/3.62 cnf(d5, plain, 'tail$uof'(sK23(sK83,sK84)) = 'head$uof'(sK84), inference(resolution, [status(thm)], [d4,c83])).
% 23.99/3.62 cnf(d6, plain, X0 != 'head$uof'(sK84) | X1 != 'head$uof'(sK23(sK83,sK84)) | 'Ts26'(sK23(sK83,sK84),X1,X0), inference(superposition, [status(thm)], [d5,c31])).
% 23.99/3.62 cnf(d7, plain, X0 != 'tail$uof'(sK83) | X1 != 'head$uof'(sK84) | 'Ts26'(sK23(sK83,sK84),X0,X1), inference(demodulation, [status(thm)], [d6,d2])).
% 23.99/3.62 cnf(d8, plain, X0 != 'head$uof'(sK84) | 'Ts26'(sK23(sK83,sK84),'tail$uof'(sK83),X0), inference(equality_resolution, [status(thm)], [d7])).
% 23.99/3.62 cnf(d9, plain, 'Ts26'(sK23(sK83,sK84),'tail$uof'(sK83),'head$uof'(sK84)), inference(equality_resolution, [status(thm)], [d8])).
% 23.99/3.62 cnf(d10, plain, 'tail$uof'(sK83) = 'head$uof'(sK23(sK83,sK84)), inference(resolution, [status(thm)], [d9,c29])).
% 23.99/3.62 cnf(d11, plain, 'tail$uof'(sK83) != 'tail$uof'(X0) | sK23(sK83,sK84) = X0 | ~edge(X0) | ~edge(sK23(sK83,sK84)) | 'Ts52'(sK23(sK83,sK84),X0), inference(superposition, [status(thm)], [d10,c60])).
% 23.99/3.62 cnf(d12, plain, edge(sK23(X0,X1)) | ~precedes(X0,X1,X2) | ~'shortest$upath'(X3,X4,X2), inference(resolution, [status(thm)], [c81,c16])).
% 23.99/3.62 cnf(d13, plain, edge(sK23(X0,X1)) | ~precedes(X0,X1,sK85), inference(resolution, [status(thm)], [d12,c82])).
% 23.99/3.62 cnf(d14, plain, edge(sK23(sK83,sK84)), inference(resolution, [status(thm)], [d13,c83])).
% 23.99/3.62 cnf(d15, plain, sK23(sK83,sK84) = X0 | 'tail$uof'(sK83) != 'tail$uof'(X0) | ~edge(X0) | 'Ts52'(sK23(sK83,sK84),X0), inference(resolution, [status(thm)], [d14,d11])).
% 23.99/3.62 cnf(d16, plain, sK23(sK83,sK84) = sK83 | ~edge(sK83) | 'Ts52'(sK23(sK83,sK84),sK83), inference(equality_resolution, [status(thm)], [d15])).
% 23.99/3.62 cnf(d17, plain, 'Ts52'(sK83,sK84), inference(resolution, [status(thm)], [c54,c84])).
% 23.99/3.62 cnf(d18, plain, edge(sK83), inference(resolution, [status(thm)], [d17,c56])).
% 23.99/3.62 cnf(d19, plain, sK23(sK83,sK84) = sK83 | 'Ts52'(sK23(sK83,sK84),sK83), inference(resolution, [status(thm)], [d18,d16])).
% 23.99/3.62 cnf(d20, plain, sK23(sK83,sK84) = sK83 | sequential(sK23(sK83,sK84),sK83), inference(resolution, [status(thm)], [d19,c55])).
% 23.99/3.62 cnf(d21, plain, 'head$uof'(sK84) = 'tail$uof'(sK23(sK83,sK84)), inference(resolution, [status(thm)], [d9,c30])).
% 23.99/3.62 cnf(d22, plain, 'head$uof'(X0) != 'head$uof'(sK84) | X0 = sK23(sK83,sK84) | ~edge(sK23(sK83,sK84)) | ~edge(X0) | 'Ts52'(X0,sK23(sK83,sK84)), inference(superposition, [status(thm)], [d21,c60])).
% 23.99/3.62 cnf(d23, plain, X0 = sK23(sK83,sK84) | 'head$uof'(X0) != 'head$uof'(sK84) | ~edge(X0) | 'Ts52'(X0,sK23(sK83,sK84)), inference(resolution, [status(thm)], [d14,d22])).
% 23.99/3.62 cnf(d24, plain, sK84 = sK23(sK83,sK84) | ~edge(sK84) | 'Ts52'(sK84,sK23(sK83,sK84)), inference(equality_resolution, [status(thm)], [d23])).
% 23.99/3.62 cnf(d25, plain, edge(sK84), inference(resolution, [status(thm)], [d17,c57])).
% 23.99/3.62 cnf(d26, plain, sK84 = sK23(sK83,sK84) | 'Ts52'(sK84,sK23(sK83,sK84)), inference(resolution, [status(thm)], [d25,d24])).
% 23.99/3.62 cnf(d27, plain, sK84 = sK23(sK83,sK84) | sequential(sK84,sK23(sK83,sK84)), inference(resolution, [status(thm)], [d26,c55])).
% 23.99/3.62 cnf(d28, plain, ~edge(X0) | ~edge(X1) | ~edge(X2) | ~sequential(X0,X2) | ~sequential(X1,X0) | ~sequential(X2,X1) | triangle(X2,X1,X0), inference(resolution, [status(thm)], [c8,c1])).
% 23.99/3.62 cnf(d29, plain, ~edge(sK83) | ~edge(sK84) | ~edge(X0) | ~sequential(sK83,sK84) | ~sequential(sK84,X0) | ~sequential(X0,sK83), inference(resolution, [status(thm)], [d28,c85])).
% 23.99/3.62 cnf(d30, plain, ~edge(X0) | ~edge(sK83) | ~edge(sK84) | ~sequential(X0,sK83) | ~sequential(sK84,X0), inference(resolution, [status(thm)], [c84,d29])).
% 23.99/3.62 cnf(d31, plain, ~edge(X0) | ~edge(sK83) | ~sequential(X0,sK83) | ~sequential(sK84,X0), inference(resolution, [status(thm)], [d25,d30])).
% 23.99/3.62 cnf(d32, plain, ~edge(X0) | ~sequential(X0,sK83) | ~sequential(sK84,X0), inference(resolution, [status(thm)], [d18,d31])).
% 23.99/3.62 cnf(d33, plain, ~edge(sK23(sK83,sK84)) | ~sequential(sK23(sK83,sK84),sK83) | sK84 = sK23(sK83,sK84), inference(resolution, [status(thm)], [d32,d27])).
% 23.99/3.62 cnf(d34, plain, sK84 = sK23(sK83,sK84) | ~sequential(sK23(sK83,sK84),sK83), inference(resolution, [status(thm)], [d14,d33])).
% 23.99/3.62 cnf(d35, plain, sK84 = sK23(sK83,sK84) | sK23(sK83,sK84) = sK83, inference(resolution, [status(thm)], [d34,d20])).
% 23.99/3.62 cnf(d36, plain, sequential(sK84,sK83) | sK23(sK83,sK84) = sK83 | sK23(sK83,sK84) = sK83, inference(superposition, [status(thm)], [d35,d20])).
% 23.99/3.62 cnf(d37, plain, ~path(X0,X1,sK85) | 'Ts61'(sK83,sK84,sK85), inference(resolution, [status(thm)], [c63,c83])).
% 23.99/3.62 cnf(d38, plain, 'Ts69'(sK85,sK81,sK82), inference(resolution, [status(thm)], [c72,c82])).
% 23.99/3.62 cnf(d39, plain, path(sK81,sK82,sK85), inference(resolution, [status(thm)], [c74,d38])).
% 23.99/3.62 cnf(d40, plain, 'Ts61'(sK83,sK84,sK85), inference(resolution, [status(thm)], [d39,d37])).
% 23.99/3.62 cnf(d41, plain, 'on$upath'(sK84,sK85), inference(resolution, [status(thm)], [d40,c65])).
% 23.99/3.62 cnf(d42, plain, ~sequential(sK83,X0) | ~sequential(sK83,sK84) | ~precedes(X0,sK84,sK85), inference(resolution, [status(thm)], [d40,c69])).
% 23.99/3.62 cnf(d43, plain, ~sequential(sK83,X0) | ~precedes(X0,sK84,sK85), inference(resolution, [status(thm)], [c84,d42])).
% 23.99/3.62 cnf(d44, plain, ~sequential(X0,sK83) | ~path(X1,X2,sK85) | ~'on$upath'(X0,sK85) | ~'on$upath'(sK84,sK85) | precedes(X0,sK84,sK85), inference(resolution, [status(thm)], [c62,c83])).
% 23.99/3.62 cnf(d45, plain, ~sequential(X0,sK83) | ~'on$upath'(X0,sK85) | ~'on$upath'(sK84,sK85) | precedes(X0,sK84,sK85), inference(resolution, [status(thm)], [d39,d44])).
% 23.99/3.62 cnf(d46, plain, ~sequential(X0,sK83) | ~'on$upath'(X0,sK85) | precedes(X0,sK84,sK85), inference(resolution, [status(thm)], [d41,d45])).
% 23.99/3.62 cnf(d47, plain, ~sequential(X0,sK83) | ~'on$upath'(X0,sK85) | ~sequential(sK83,X0), inference(resolution, [status(thm)], [d46,d43])).
% 23.99/3.62 cnf(d48, plain, ~sequential(sK84,sK83) | ~sequential(sK83,sK84), inference(resolution, [status(thm)], [d47,d41])).
% 23.99/3.62 cnf(d49, plain, ~sequential(sK84,sK83), inference(resolution, [status(thm)], [c84,d48])).
% 23.99/3.62 cnf(d50, plain, sK23(sK83,sK84) = sK83, inference(resolution, [status(thm)], [d49,d36])).
% 23.99/3.62 cnf(d51, plain, 'tail$uof'(sK83) = 'head$uof'(sK83), inference(demodulation, [status(thm)], [d10,d50])).
% 23.99/3.62 cnf(d52, plain, 'tail$uof'(sK83) = 'head$uof'(sK84), inference(demodulation, [status(thm)], [d5,d50])).
% 23.99/3.62 cnf(d53, plain, 'head$uof'(sK83) = 'head$uof'(sK84), inference(demodulation, [status(thm)], [d52,d51])).
% 23.99/3.62 cnf(d54, plain, 'head$uof'(sK84) = 'tail$uof'(sK83), inference(demodulation, [status(thm)], [d21,d50])).
% 23.99/3.62 cnf(d55, plain, 'head$uof'(sK23(sK83,sK84)) != 'head$uof'(sK84) | ~edge(sK23(sK83,sK84)), inference(superposition, [status(thm)], [d5,c19])).
% 23.99/3.62 cnf(d56, plain, 'tail$uof'(sK83) != 'head$uof'(sK84) | ~edge(sK23(sK83,sK84)), inference(demodulation, [status(thm)], [d55,d2])).
% 23.99/3.62 cnf(d57, plain, 'tail$uof'(sK83) != 'head$uof'(sK84), inference(resolution, [status(thm)], [d14,d56])).
% 23.99/3.62 cnf(d58, plain, 'head$uof'(sK84) != 'head$uof'(sK84), inference(demodulation, [status(thm)], [d57,d54])).
% 23.99/3.62 cnf(d59, plain, 'head$uof'(sK83) != 'head$uof'(sK84), inference(demodulation, [status(thm)], [d58,d53])).
% 23.99/3.62 cnf(d60, plain, 'head$uof'(sK83) != 'head$uof'(sK83), inference(demodulation, [status(thm)], [d59,d53])).
% 23.99/3.62 cnf(d61, plain, $false, inference(equality_resolution, [status(thm)], [d60])).
% 23.99/3.62 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------