%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Thu Sep 24 12:02:28 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n010.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 13:21:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.39 fof(f1,axiom,(
% 0.14/0.39 (![Z,X,Y]: (( ~ less_or_equal(Z,minimum(X,Y))| less_or_equal(Z,X) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f2,axiom,(
% 0.14/0.39 (![Z,X,Y]: (( ~ less_or_equal(Z,minimum(X,Y))| less_or_equal(Z,Y) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f3,axiom,(
% 0.14/0.39 (![X,Y]: (( less_or_equal(X,n0)| less_or_equal(Y,n0)| ~ less_or_equal(minimum(X,Y),n0) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f4,axiom,(
% 0.14/0.39 (![X,Z,Y]: (( ~ less_or_equal(X,half(Z))| ~ less_or_equal(Y,half(Z))| less_or_equal(add(X,Y),Z) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f5,axiom,(
% 0.14/0.39 (![X]: (( less_or_equal(X,n0)| ~ less_or_equal(half(X),n0) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f6,hypothesis,(
% 0.14/0.39 (![Epsilon]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(delta_1(Epsilon),n0) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f7,hypothesis,(
% 0.14/0.39 (![Epsilon]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(delta_2(Epsilon),n0) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f8,hypothesis,(
% 0.14/0.39 (![Epsilon,Z]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_1(Epsilon))| less_or_equal(absolute(add(f(Z),negate(f(a_real_number)))),Epsilon) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f9,hypothesis,(
% 0.14/0.39 (![Epsilon,Z]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_2(Epsilon))| less_or_equal(absolute(add(g(Z),negate(g(a_real_number)))),Epsilon) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f10,hypothesis,(
% 0.14/0.39 ~ less_or_equal(epsilon_0,n0) ),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f11,hypothesis,(
% 0.14/0.39 (![Delta]: (( less_or_equal(Delta,n0)| less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f12,negated_conjecture,(
% 0.14/0.39 (![Delta]: (( less_or_equal(Delta,n0)| ~ less_or_equal(add(absolute(add(f(xs(Delta)),negate(f(a_real_number)))),absolute(add(g(xs(Delta)),negate(g(a_real_number))))),epsilon_0) ) ))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f13,plain,(
% 0.14/0.39 ![Z,X]: ((![Y]: ~less_or_equal(Z,minimum(X,Y)))|less_or_equal(Z,X))),
% 0.14/0.39 inference(miniscoping,[status(thm)],[f1])).
% 0.14/0.39 fof(f14,plain,(
% 0.14/0.39 ![X0,X1,X2]: (~less_or_equal(X0,minimum(X1,X2))|less_or_equal(X0,X1))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.39 fof(f15,plain,(
% 0.14/0.39 ![Z,Y]: ((![X]: ~less_or_equal(Z,minimum(X,Y)))|less_or_equal(Z,Y))),
% 0.14/0.39 inference(miniscoping,[status(thm)],[f2])).
% 0.14/0.39 fof(f16,plain,(
% 0.14/0.39 ![X0,X1,X2]: (~less_or_equal(X0,minimum(X1,X2))|less_or_equal(X0,X2))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f15])).
% 0.14/0.39 fof(f17,plain,(
% 0.14/0.39 ![X0,X1]: (less_or_equal(X0,n0)|less_or_equal(X1,n0)|~less_or_equal(minimum(X0,X1),n0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.39 fof(f18,plain,(
% 0.14/0.39 ![X0,X1,X2]: (~less_or_equal(X0,half(X1))|~less_or_equal(X2,half(X1))|less_or_equal(add(X0,X2),X1))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.39 fof(f19,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(half(X0),n0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.39 fof(f20,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(delta_1(X0),n0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.39 fof(f21,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(delta_2(X0),n0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.14/0.39 fof(f22,plain,(
% 0.14/0.39 ![X0,X1]: (less_or_equal(X0,n0)|~less_or_equal(absolute(add(X1,negate(a_real_number))),delta_1(X0))|less_or_equal(absolute(add(f(X1),negate(f(a_real_number)))),X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.39 fof(f23,plain,(
% 0.14/0.39 ![X0,X1]: (less_or_equal(X0,n0)|~less_or_equal(absolute(add(X1,negate(a_real_number))),delta_2(X0))|less_or_equal(absolute(add(g(X1),negate(g(a_real_number)))),X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/0.39 fof(f24,plain,(
% 0.14/0.39 ~less_or_equal(epsilon_0,n0)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/0.39 fof(f25,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.39 fof(f26,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(add(absolute(add(f(xs(X0)),negate(f(a_real_number)))),absolute(add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/0.39 fof(f27,plain,(
% 0.14/0.39 ![X0,X1]: (less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0)|less_or_equal(minimum(X0,X1),n0))),
% 0.14/0.39 inference(resolution,[status(thm)],[f14,f25])).
% 0.14/0.39 fof(f44,plain,(
% 0.14/0.39 ![X0,X1]: (less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1)|less_or_equal(minimum(X0,X1),n0))),
% 0.14/0.39 inference(resolution,[status(thm)],[f16,f25])).
% 0.14/0.39 fof(f45,plain,(
% 0.14/0.39 ![X0]: (~less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))|~less_or_equal(absolute(add(g(xs(X0)),negate(g(a_real_number)))),half(epsilon_0))|less_or_equal(X0,n0))),
% 0.14/0.39 inference(resolution,[status(thm)],[f18,f26])).
% 0.14/0.39 fof(f60,plain,(
% 0.14/0.39 ![X0]: (~less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))|less_or_equal(X0,n0)|less_or_equal(half(epsilon_0),n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0))))),
% 0.14/0.39 inference(resolution,[status(thm)],[f45,f23])).
% 0.14/0.39 fof(f61,definition,(
% 0.14/0.39 ![X0]: (sQ0_spl <=> (~less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))|less_or_equal(X0,n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f62,plain,(
% 0.14/0.39 ![X0]: (~less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))|less_or_equal(X0,n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))|~sQ0_spl)),
% 0.14/0.39 inference(component_clause,[status(thm)],[f61])).
% 0.14/0.39 fof(f64,definition,(
% 0.14/0.39 sQ1_spl <=> (less_or_equal(half(epsilon_0),n0))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f65,plain,(
% 0.14/0.39 less_or_equal(half(epsilon_0),n0)|~sQ1_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f64])).
% 0.14/0.39 fof(f67,plain,(
% 0.14/0.39 sQ0_spl|sQ1_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f60,f61,f64])).
% 0.14/0.39 fof(f68,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))|less_or_equal(half(epsilon_0),n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))|~sQ0_spl)),
% 0.14/0.39 inference(resolution,[status(thm)],[f62,f22])).
% 0.14/0.39 fof(f69,definition,(
% 0.14/0.39 ![X0]: (sQ2_spl <=> (less_or_equal(X0,n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f70,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))|~less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))|~sQ2_spl)),
% 0.14/0.39 inference(component_clause,[status(thm)],[f69])).
% 0.14/0.39 fof(f72,plain,(
% 0.14/0.39 sQ2_spl|sQ1_spl|~sQ0_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f68,f69,f64,f61])).
% 0.14/0.39 fof(f73,plain,(
% 0.14/0.39 less_or_equal(epsilon_0,n0)|~sQ1_spl),
% 0.14/0.39 inference(resolution,[status(thm)],[f65,f19])).
% 0.14/0.39 fof(f74,plain,(
% 0.14/0.39 $false|~sQ1_spl),
% 0.14/0.39 inference(forward_subsumption_resolution,[status(thm)],[f73,f24])).
% 0.14/0.39 fof(f75,plain,(
% 0.14/0.39 ~sQ1_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f74])).
% 0.14/0.39 fof(f195,plain,(
% 0.14/0.39 ![X0]: (less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0)|~less_or_equal(absolute(add(xs(minimum(X0,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))|less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0)|~sQ2_spl)),
% 0.14/0.40 inference(resolution,[status(thm)],[f70,f44])).
% 0.14/0.40 fof(f215,plain,(
% 0.14/0.40 ![X0]: (less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0)|~less_or_equal(absolute(add(xs(minimum(X0,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))|~sQ2_spl)),
% 0.14/0.40 inference(duplicate_literals_removal,[status(thm)],[f195])).
% 0.14/0.40 fof(f217,definition,(
% 0.14/0.40 sQ3_spl <=> (less_or_equal(delta_2(half(epsilon_0)),n0))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f218,plain,(
% 0.14/0.40 less_or_equal(delta_2(half(epsilon_0)),n0)|~sQ3_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f217])).
% 0.14/0.40 fof(f224,plain,(
% 0.14/0.40 less_or_equal(half(epsilon_0),n0)|~sQ3_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f218,f21])).
% 0.14/0.40 fof(f225,plain,(
% 0.14/0.40 sQ1_spl|~sQ3_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f224,f64,f217])).
% 0.14/0.40 fof(f349,plain,(
% 0.14/0.40 less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)|less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)|~sQ2_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f215,f27])).
% 0.14/0.40 fof(f361,definition,(
% 0.14/0.40 sQ5_spl <=> (less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f362,plain,(
% 0.14/0.40 less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)|~sQ5_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f361])).
% 0.14/0.40 fof(f364,plain,(
% 0.14/0.40 sQ5_spl|~sQ2_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f349,f361,f69])).
% 0.14/0.40 fof(f387,plain,(
% 0.14/0.40 less_or_equal(delta_1(half(epsilon_0)),n0)|less_or_equal(delta_2(half(epsilon_0)),n0)|~sQ5_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f362,f17])).
% 0.14/0.40 fof(f388,definition,(
% 0.14/0.40 sQ6_spl <=> (less_or_equal(delta_1(half(epsilon_0)),n0))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f389,plain,(
% 0.14/0.40 less_or_equal(delta_1(half(epsilon_0)),n0)|~sQ6_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f388])).
% 0.14/0.40 fof(f391,plain,(
% 0.14/0.40 sQ6_spl|sQ3_spl|~sQ5_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f387,f388,f217,f361])).
% 0.14/0.40 fof(f392,plain,(
% 0.14/0.40 less_or_equal(half(epsilon_0),n0)|~sQ6_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f389,f20])).
% 0.14/0.40 fof(f393,plain,(
% 0.14/0.40 sQ1_spl|~sQ6_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f392,f64,f388])).
% 0.14/0.40 fof(f394,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(sat_refutation,[status(thm)],[f67,f72,f75,f225,f364,f391,f393])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.41 % Elapsed time: 0.051729 seconds
% 0.14/0.41 % CPU time: 0.203178 seconds
% 0.14/0.41 % Total memory used: 14.823 MB
% 0.14/0.41 % Net memory used: 14.503 MB
%------------------------------------------------------------------------------