%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA004+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 : n004.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 6.77s 3.62s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA004+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
% 0.09/0.57 % Computer : n004.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Fri Sep 25 13:48:09 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/3.62 % SZS status Theorem for theBenchmark.p
% 6.77/3.62 % SZS output start CNFRefutation for theBenchmark.p
% 6.77/3.62 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)))))))))).
% 6.77/3.62 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$uof'(X3),X2)))))).
% 6.77/3.62 fof(sequential_defn, axiom, ! [X0] : ! [X1] : ((sequential(X0,X1) <=> (edge(X0) & (edge(X1) & (X0 != X1 & 'head$uof'(X0) = 'tail$uof'(X1))))))).
% 6.77/3.62 fof(precedes_defn, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X1,X2,X0) => ! [X3] : ! [X4] : ((('on$upath'(X3,X0) & ('on$upath'(X4,X0) & (sequential(X3,X4) | ? [X5] : ((sequential(X3,X5) & precedes(X5,X4,X0)))))) => precedes(X3,X4,X0)))))).
% 6.77/3.62 fof(precedes_properties, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X1,X2,X0) => ! [X3] : ! [X4] : ((precedes(X3,X4,X0) => ('on$upath'(X3,X0) & ('on$upath'(X4,X0) & ~((sequential(X3,X4) <=> ? [X5] : ((sequential(X3,X5) & precedes(X5,X4,X0)))))))))))).
% 6.77/3.62 fof(shortest_path_defn, axiom, ! [X0] : ! [X1] : ! [X2] : (('shortest$upath'(X0,X1,X2) <=> (path(X0,X1,X2) & (X0 != X1 & ! [X3] : ((path(X0,X1,X3) => 'less$uor$uequal'('length$uof'(X2),'length$uof'(X3))))))))).
% 6.77/3.62 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$uof'(X3))) & ~precedes(X3,X2,X4))))).
% 6.77/3.62 fof(shortest_path_properties_lemma, conjecture, ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & precedes(X2,X3,X4)) => (~? [X5] : (('tail$uof'(X5) = 'tail$uof'(X2) & 'head$uof'(X5) = 'head$uof'(X3))) & ('head$uof'(X3) != 'tail$uof'(X2) & 'head$uof'(X3) != 'head$uof'(X2)))))).
% 6.77/3.62 fof(negated_conjecture, negated_conjecture, ~! [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$uof'(X3))) & ('head$uof'(X3) != 'tail$uof'(X2) & 'head$uof'(X3) != 'head$uof'(X2))))), inference(negate_conjecture, [status(cth)], [shortest_path_properties_lemma])).
% 6.77/3.62 cnf(c26, plain, ~X0(X1,X2,X3) | X2 = 'head$uof'(X1), inference(clausification, [status(esa)], [complete_properties])).
% 6.77/3.62 cnf(c28, plain, X0(X1,X2,X3) | X2 != 'head$uof'(X1) | X3 != 'tail$uof'(X1), inference(clausification, [status(esa)], [complete_properties])).
% 6.77/3.62 cnf(c45, plain, ~path(X0,X1,X2) | ~'on$upath'(X3,X2) | edge(X3), inference(clausification, [status(esa)], [on_path_properties])).
% 6.77/3.62 cnf(c52, plain, sequential(X0,X1) | ~X2(X0,X1), inference(clausification, [status(esa)], [sequential_defn])).
% 6.77/3.62 cnf(c57, plain, 'head$uof'(X0) != 'tail$uof'(X1) | ~edge(X0) | ~edge(X1) | X0 = X1 | X2(X0,X1), inference(clausification, [status(esa)], [sequential_defn])).
% 6.77/3.62 cnf(c58, plain, ~sequential(X0,X1) | ~'on$upath'(X0,X2) | ~'on$upath'(X1,X2) | ~path(X3,X4,X2) | precedes(X0,X1,X2), inference(clausification, [status(esa)], [precedes_defn])).
% 6.77/3.62 cnf(c60, plain, ~path(X0,X1,X2) | ~precedes(X3,X4,X2) | X5(X3,X4,X2), inference(clausification, [status(esa)], [precedes_properties])).
% 6.77/3.62 cnf(c61, plain, ~X0(X1,X2,X3) | 'on$upath'(X1,X3), inference(clausification, [status(esa)], [precedes_properties])).
% 6.77/3.62 cnf(c62, plain, ~X0(X1,X2,X3) | 'on$upath'(X2,X3), inference(clausification, [status(esa)], [precedes_properties])).
% 6.77/3.62 cnf(c69, plain, ~'shortest$upath'(X0,X1,X2) | X3(X2,X0,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 6.77/3.62 cnf(c71, plain, ~X0(X1,X2,X3) | path(X2,X3,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 6.77/3.62 cnf(c76, plain, ~'shortest$upath'(X0,X1,X2) | ~precedes(X3,X4,X2) | 'tail$uof'(X5) != 'tail$uof'(X3) | 'head$uof'(X5) != 'head$uof'(X4), inference(clausification, [status(esa)], [shortest_path_properties])).
% 6.77/3.62 cnf(c77, plain, ~'shortest$upath'(X0,X1,X2) | ~precedes(X3,X4,X2) | ~precedes(X4,X3,X2), inference(clausification, [status(esa)], [shortest_path_properties])).
% 6.77/3.62 cnf(c78, plain, 'shortest$upath'(sK75,sK76,sK79), inference(clausification, [status(esa)], [negated_conjecture])).
% 6.77/3.62 cnf(c79, plain, precedes(sK77,sK78,sK79), inference(clausification, [status(esa)], [negated_conjecture])).
% 6.77/3.62 cnf(c80, plain, 'tail$uof'(sK80) = 'tail$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77) | 'head$uof'(sK78) = 'head$uof'(sK77), inference(clausification, [status(esa)], [negated_conjecture])).
% 6.77/3.62 cnf(c81, plain, 'head$uof'(sK80) = 'head$uof'(sK78) | 'head$uof'(sK78) = 'tail$uof'(sK77) | 'head$uof'(sK78) = 'head$uof'(sK77), inference(clausification, [status(esa)], [negated_conjecture])).
% 6.77/3.62 cnf(d0, plain, 'head$uof'(X0) != 'head$uof'(X1) | ~precedes(X0,X1,X2) | ~'shortest$upath'(X3,X4,X2), inference(equality_resolution, [status(thm)], [c76])).
% 6.77/3.62 cnf(d1, plain, 'tail$uof'(sK77) != 'tail$uof'(X0) | 'head$uof'(sK80) != 'head$uof'(X1) | ~precedes(X0,X1,X2) | ~'shortest$upath'(X3,X4,X2) | 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77), inference(superposition, [status(thm)], [c80,c76])).
% 6.77/3.62 cnf(d2, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77) | 'head$uof'(sK80) != 'head$uof'(X0) | ~precedes(sK77,X0,X1) | ~'shortest$upath'(X2,X3,X1), inference(equality_resolution, [status(thm)], [d1])).
% 6.77/3.62 cnf(d3, plain, X0 != 'head$uof'(X1) | 'Ts20'(X1,X0,'tail$uof'(X1)), inference(equality_resolution, [status(thm)], [c28])).
% 6.77/3.62 cnf(d4, plain, 'Ts20'(X0,'head$uof'(X0),'tail$uof'(X0)), inference(equality_resolution, [status(thm)], [d3])).
% 6.77/3.62 cnf(d5, plain, 'head$uof'(X0) != 'head$uof'(sK78) | X0 = sK77 | ~edge(sK77) | ~edge(X0) | 'Ts46'(X0,sK77) | 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK80) = 'head$uof'(sK78), inference(superposition, [status(thm)], [c81,c57])).
% 6.77/3.62 cnf(d6, plain, 'Ts63'(sK79,sK75,sK76), inference(resolution, [status(thm)], [c69,c78])).
% 6.77/3.62 cnf(d7, plain, path(sK75,sK76,sK79), inference(resolution, [status(thm)], [c71,d6])).
% 6.77/3.62 cnf(d8, plain, edge(X0) | ~'on$upath'(X0,sK79), inference(resolution, [status(thm)], [d7,c45])).
% 6.77/3.62 cnf(d9, plain, ~path(X0,X1,sK79) | 'Ts55'(sK77,sK78,sK79), inference(resolution, [status(thm)], [c60,c79])).
% 6.77/3.62 cnf(d10, plain, 'Ts55'(sK77,sK78,sK79), inference(resolution, [status(thm)], [d9,d7])).
% 6.77/3.62 cnf(d11, plain, 'on$upath'(sK77,sK79), inference(resolution, [status(thm)], [d10,c61])).
% 6.77/3.62 cnf(d12, plain, edge(sK77), inference(resolution, [status(thm)], [d11,d8])).
% 6.77/3.62 cnf(d13, plain, X0 = sK77 | 'head$uof'(X0) != 'head$uof'(sK78) | 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK80) = 'head$uof'(sK78) | ~edge(X0) | 'Ts46'(X0,sK77), inference(resolution, [status(thm)], [d12,d5])).
% 6.77/3.62 cnf(d14, plain, sK78 = sK77 | 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK80) = 'head$uof'(sK78) | ~edge(sK78) | 'Ts46'(sK78,sK77), inference(equality_resolution, [status(thm)], [d13])).
% 6.77/3.62 cnf(d15, plain, 'on$upath'(sK78,sK79), inference(resolution, [status(thm)], [d10,c62])).
% 6.77/3.62 cnf(d16, plain, edge(sK78), inference(resolution, [status(thm)], [d15,d8])).
% 6.77/3.62 cnf(d17, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK80) = 'head$uof'(sK78) | sK78 = sK77 | 'Ts46'(sK78,sK77), inference(resolution, [status(thm)], [d16,d14])).
% 6.77/3.62 cnf(d18, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK80) = 'head$uof'(sK78) | sK78 = sK77 | sequential(sK78,sK77), inference(resolution, [status(thm)], [d17,c52])).
% 6.77/3.62 cnf(d19, plain, ~precedes(X0,X1,sK79) | ~precedes(X1,X0,sK79), inference(resolution, [status(thm)], [c77,c78])).
% 6.77/3.62 cnf(d20, plain, ~precedes(sK78,sK77,sK79), inference(resolution, [status(thm)], [d19,c79])).
% 6.77/3.62 cnf(d21, plain, ~sequential(X0,X1) | ~'on$upath'(X0,sK79) | ~'on$upath'(X1,sK79) | precedes(X0,X1,sK79), inference(resolution, [status(thm)], [c58,d7])).
% 6.77/3.62 cnf(d22, plain, ~sequential(sK78,sK77) | ~'on$upath'(sK77,sK79) | ~'on$upath'(sK78,sK79), inference(resolution, [status(thm)], [d21,d20])).
% 6.77/3.62 cnf(d23, plain, ~sequential(sK78,sK77) | ~'on$upath'(sK77,sK79), inference(resolution, [status(thm)], [d15,d22])).
% 6.77/3.62 cnf(d24, plain, ~sequential(sK78,sK77), inference(resolution, [status(thm)], [d11,d23])).
% 6.77/3.62 cnf(d25, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK80) = 'head$uof'(sK78) | sK78 = sK77, inference(resolution, [status(thm)], [d24,d18])).
% 6.77/3.62 cnf(d26, plain, 'Ts20'(sK80,'head$uof'(sK78),'tail$uof'(sK80)) | 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77, inference(superposition, [status(thm)], [d25,d4])).
% 6.77/3.62 cnf(d27, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77 | 'head$uof'(sK78) = 'head$uof'(sK80), inference(resolution, [status(thm)], [d26,c26])).
% 6.77/3.62 cnf(d28, plain, 'head$uof'(sK78) != 'head$uof'(X0) | 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77) | ~precedes(sK77,X0,X1) | ~'shortest$upath'(X2,X3,X1) | 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77, inference(superposition, [status(thm)], [d27,d2])).
% 6.77/3.62 cnf(d29, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77) | sK78 = sK77 | ~precedes(sK77,sK78,X0) | ~'shortest$upath'(X1,X2,X0), inference(equality_resolution, [status(thm)], [d28])).
% 6.77/3.62 cnf(d30, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77) | sK78 = sK77 | ~precedes(sK77,sK78,sK79), inference(resolution, [status(thm)], [d29,c78])).
% 6.77/3.62 cnf(d31, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | 'head$uof'(sK78) = 'tail$uof'(sK77) | sK78 = sK77, inference(resolution, [status(thm)], [c79,d30])).
% 6.77/3.62 cnf(d32, plain, 'head$uof'(X0) != 'head$uof'(sK78) | X0 = sK77 | ~edge(sK77) | ~edge(X0) | 'Ts46'(X0,sK77) | 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77, inference(superposition, [status(thm)], [d31,c57])).
% 6.77/3.62 cnf(d33, plain, X0 = sK77 | 'head$uof'(X0) != 'head$uof'(sK78) | 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77 | ~edge(X0) | 'Ts46'(X0,sK77), inference(resolution, [status(thm)], [d12,d32])).
% 6.77/3.62 cnf(d34, plain, sK78 = sK77 | 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77 | ~edge(sK78) | 'Ts46'(sK78,sK77), inference(equality_resolution, [status(thm)], [d33])).
% 6.77/3.62 cnf(d35, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77 | 'Ts46'(sK78,sK77), inference(resolution, [status(thm)], [d16,d34])).
% 6.77/3.62 cnf(d36, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77 | sequential(sK78,sK77), inference(resolution, [status(thm)], [d35,c52])).
% 6.77/3.62 cnf(d37, plain, 'head$uof'(sK78) = 'head$uof'(sK77) | sK78 = sK77, inference(resolution, [status(thm)], [d24,d36])).
% 6.77/3.62 cnf(d38, plain, 'head$uof'(X0) != 'head$uof'(sK77) | ~precedes(X0,sK78,X1) | ~'shortest$upath'(X2,X3,X1) | sK78 = sK77, inference(superposition, [status(thm)], [d37,d0])).
% 6.77/3.62 cnf(d39, plain, sK78 = sK77 | ~precedes(sK77,sK78,X0) | ~'shortest$upath'(X1,X2,X0), inference(equality_resolution, [status(thm)], [d38])).
% 6.77/3.62 cnf(d40, plain, sK78 = sK77 | ~precedes(sK77,sK78,sK79), inference(resolution, [status(thm)], [d39,c78])).
% 6.77/3.62 cnf(d41, plain, sK78 = sK77, inference(resolution, [status(thm)], [c79,d40])).
% 6.77/3.62 cnf(d42, plain, precedes(sK77,sK77,sK79), inference(demodulation, [status(thm)], [c79,d41])).
% 6.77/3.62 cnf(d43, plain, ~precedes(X0,X0,X1) | ~'shortest$upath'(X2,X3,X1), inference(equality_resolution, [status(thm)], [d0])).
% 6.77/3.62 cnf(d44, plain, ~precedes(X0,X0,sK79), inference(resolution, [status(thm)], [d43,c78])).
% 6.77/3.62 cnf(d45, plain, $false, inference(resolution, [status(thm)], [d44,d42])).
% 6.77/3.62 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------