%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.15s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n018.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 13:24:13 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.48 fof(f1,axiom,(
% 0.15/0.48 (![X,Y,Z]: (( ~ less_or_equal(add(absolute(X),absolute(Y)),Z)| less_or_equal(absolute(add(X,Y)),Z) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f2,axiom,(
% 0.15/0.48 (![Z,X,Y]: (( ~ less_or_equal(Z,minimum(X,Y))| less_or_equal(Z,X) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f3,axiom,(
% 0.15/0.48 (![Z,X,Y]: (( ~ less_or_equal(Z,minimum(X,Y))| less_or_equal(Z,Y) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f4,axiom,(
% 0.15/0.48 (![X,Y]: (( less_or_equal(X,n0)| less_or_equal(Y,n0)| ~ less_or_equal(minimum(X,Y),n0) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f5,axiom,(
% 0.15/0.48 (![X,Z,Y]: (( ~ less_or_equal(X,half(Z))| ~ less_or_equal(Y,half(Z))| less_or_equal(add(X,Y),Z) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f6,axiom,(
% 0.15/0.48 (![X]: (( less_or_equal(X,n0)| ~ less_or_equal(half(X),n0) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f7,hypothesis,(
% 0.15/0.48 (![Epsilon]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(delta_1(Epsilon),n0) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f8,hypothesis,(
% 0.15/0.48 (![Epsilon]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(delta_2(Epsilon),n0) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f9,hypothesis,(
% 0.15/0.48 (![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) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f10,hypothesis,(
% 0.15/0.48 (![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) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f11,hypothesis,(
% 0.15/0.48 ~ less_or_equal(epsilon_0,n0) ),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f12,hypothesis,(
% 0.15/0.48 (![Delta]: (( less_or_equal(Delta,n0)| less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f13,negated_conjecture,(
% 0.15/0.48 (![Delta]: (( less_or_equal(Delta,n0)| ~ less_or_equal(absolute(add(add(f(xs(Delta)),negate(f(a_real_number))),add(g(xs(Delta)),negate(g(a_real_number))))),epsilon_0) ) ))),
% 0.15/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f14,plain,(
% 0.15/0.48 ![X0,X1,X2]: (~less_or_equal(add(absolute(X0),absolute(X1)),X2)|less_or_equal(absolute(add(X0,X1)),X2))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.15/0.48 fof(f15,plain,(
% 0.15/0.48 ![Z,X]: ((![Y]: ~less_or_equal(Z,minimum(X,Y)))|less_or_equal(Z,X))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f2])).
% 0.15/0.48 fof(f16,plain,(
% 0.15/0.48 ![X0,X1,X2]: (~less_or_equal(X0,minimum(X1,X2))|less_or_equal(X0,X1))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f15])).
% 0.15/0.48 fof(f17,plain,(
% 0.15/0.48 ![Z,Y]: ((![X]: ~less_or_equal(Z,minimum(X,Y)))|less_or_equal(Z,Y))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f3])).
% 0.15/0.48 fof(f18,plain,(
% 0.15/0.48 ![X0,X1,X2]: (~less_or_equal(X0,minimum(X1,X2))|less_or_equal(X0,X2))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f17])).
% 0.15/0.48 fof(f19,plain,(
% 0.15/0.48 ![X0,X1]: (less_or_equal(X0,n0)|less_or_equal(X1,n0)|~less_or_equal(minimum(X0,X1),n0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.15/0.48 fof(f20,plain,(
% 0.15/0.48 ![X0,X1,X2]: (~less_or_equal(X0,half(X1))|~less_or_equal(X2,half(X1))|less_or_equal(add(X0,X2),X1))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f5])).
% 0.15/0.48 fof(f21,plain,(
% 0.15/0.48 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(half(X0),n0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f6])).
% 0.15/0.48 fof(f22,plain,(
% 0.15/0.48 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(delta_1(X0),n0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f7])).
% 0.15/0.48 fof(f23,plain,(
% 0.15/0.48 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(delta_2(X0),n0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f8])).
% 0.15/0.48 fof(f24,plain,(
% 0.15/0.48 ![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))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/0.48 fof(f25,plain,(
% 0.15/0.48 ![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))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f10])).
% 0.15/0.48 fof(f26,plain,(
% 0.15/0.48 ~less_or_equal(epsilon_0,n0)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f11])).
% 0.15/0.48 fof(f27,plain,(
% 0.15/0.48 ![X0]: (less_or_equal(X0,n0)|less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.15/0.48 fof(f28,plain,(
% 0.15/0.48 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(absolute(add(add(f(xs(X0)),negate(f(a_real_number))),add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f13])).
% 0.15/0.48 fof(f29,plain,(
% 0.15/0.48 ![X0,X1]: (less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0)|less_or_equal(minimum(X0,X1),n0))),
% 0.15/0.48 inference(resolution,[status(thm)],[f16,f27])).
% 0.15/0.48 fof(f44,plain,(
% 0.15/0.48 ![X0,X1]: (less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1)|less_or_equal(minimum(X0,X1),n0))),
% 0.15/0.48 inference(resolution,[status(thm)],[f18,f27])).
% 0.15/0.48 fof(f45,plain,(
% 0.15/0.48 ![X0,X1,X2]: (~less_or_equal(absolute(X0),half(X1))|~less_or_equal(absolute(X2),half(X1))|less_or_equal(absolute(add(X0,X2)),X1))),
% 0.15/0.48 inference(resolution,[status(thm)],[f20,f14])).
% 0.15/0.48 fof(f50,plain,(
% 0.15/0.48 ![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))),
% 0.15/0.48 inference(resolution,[status(thm)],[f45,f28])).
% 0.15/0.48 fof(f63,plain,(
% 0.15/0.48 ![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))))),
% 0.15/0.48 inference(resolution,[status(thm)],[f50,f25])).
% 0.15/0.48 fof(f65,definition,(
% 0.15/0.48 ![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)))))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.48 fof(f66,plain,(
% 0.15/0.48 ![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)),
% 0.15/0.48 inference(component_clause,[status(thm)],[f65])).
% 0.15/0.48 fof(f68,definition,(
% 0.15/0.48 sQ1_spl <=> (less_or_equal(half(epsilon_0),n0))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.48 fof(f69,plain,(
% 0.15/0.48 less_or_equal(half(epsilon_0),n0)|~sQ1_spl),
% 0.15/0.48 inference(component_clause,[status(thm)],[f68])).
% 0.15/0.48 fof(f71,plain,(
% 0.15/0.48 sQ0_spl|sQ1_spl),
% 0.15/0.48 inference(split_clause,[status(thm)],[f63,f65,f68])).
% 0.15/0.48 fof(f79,plain,(
% 0.15/0.48 ![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)),
% 0.15/0.48 inference(resolution,[status(thm)],[f66,f24])).
% 0.15/0.48 fof(f81,definition,(
% 0.15/0.48 ![X0]: (sQ4_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)))))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/0.48 fof(f82,plain,(
% 0.15/0.48 ![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)))|~sQ4_spl)),
% 0.15/0.48 inference(component_clause,[status(thm)],[f81])).
% 0.15/0.48 fof(f84,plain,(
% 0.15/0.48 sQ4_spl|sQ1_spl|~sQ0_spl),
% 0.15/0.48 inference(split_clause,[status(thm)],[f79,f81,f68,f65])).
% 0.15/0.48 fof(f92,plain,(
% 0.15/0.48 less_or_equal(epsilon_0,n0)|~sQ1_spl),
% 0.15/0.48 inference(resolution,[status(thm)],[f69,f21])).
% 0.15/0.48 fof(f93,plain,(
% 0.15/0.48 $false|~sQ1_spl),
% 0.15/0.48 inference(forward_subsumption_resolution,[status(thm)],[f92,f26])).
% 0.15/0.48 fof(f94,plain,(
% 0.15/0.48 ~sQ1_spl),
% 0.15/0.48 inference(contradiction_clause,[status(thm)],[f93])).
% 0.15/0.48 fof(f208,plain,(
% 0.15/0.48 ![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)|~sQ4_spl)),
% 0.15/0.48 inference(resolution,[status(thm)],[f82,f44])).
% 0.15/0.48 fof(f228,plain,(
% 0.15/0.48 ![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)))|~sQ4_spl)),
% 0.15/0.48 inference(duplicate_literals_removal,[status(thm)],[f208])).
% 0.15/0.48 fof(f230,definition,(
% 0.15/0.48 sQ7_spl <=> (less_or_equal(delta_2(half(epsilon_0)),n0))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.15/0.48 fof(f231,plain,(
% 0.15/0.48 less_or_equal(delta_2(half(epsilon_0)),n0)|~sQ7_spl),
% 0.15/0.48 inference(component_clause,[status(thm)],[f230])).
% 0.15/0.48 fof(f244,plain,(
% 0.15/0.48 less_or_equal(half(epsilon_0),n0)|~sQ7_spl),
% 0.15/0.48 inference(resolution,[status(thm)],[f231,f23])).
% 0.15/0.48 fof(f245,plain,(
% 0.15/0.48 sQ1_spl|~sQ7_spl),
% 0.15/0.48 inference(split_clause,[status(thm)],[f244,f68,f230])).
% 0.15/0.48 fof(f459,plain,(
% 0.15/0.48 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)|~sQ4_spl),
% 0.15/0.48 inference(resolution,[status(thm)],[f228,f29])).
% 0.15/0.48 fof(f477,definition,(
% 0.15/0.48 sQ15_spl <=> (less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.15/0.48 fof(f478,plain,(
% 0.15/0.48 less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)|~sQ15_spl),
% 0.15/0.48 inference(component_clause,[status(thm)],[f477])).
% 0.15/0.48 fof(f480,plain,(
% 0.15/0.48 sQ15_spl|~sQ4_spl),
% 0.15/0.48 inference(split_clause,[status(thm)],[f459,f477,f81])).
% 0.15/0.48 fof(f485,plain,(
% 0.15/0.48 less_or_equal(delta_1(half(epsilon_0)),n0)|less_or_equal(delta_2(half(epsilon_0)),n0)|~sQ15_spl),
% 0.15/0.48 inference(resolution,[status(thm)],[f478,f19])).
% 0.15/0.48 fof(f486,definition,(
% 0.15/0.48 sQ17_spl <=> (less_or_equal(delta_1(half(epsilon_0)),n0))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.15/0.48 fof(f487,plain,(
% 0.15/0.48 less_or_equal(delta_1(half(epsilon_0)),n0)|~sQ17_spl),
% 0.15/0.48 inference(component_clause,[status(thm)],[f486])).
% 0.15/0.48 fof(f489,plain,(
% 0.15/0.48 sQ17_spl|sQ7_spl|~sQ15_spl),
% 0.15/0.48 inference(split_clause,[status(thm)],[f485,f486,f230,f477])).
% 0.15/0.48 fof(f508,plain,(
% 0.15/0.48 less_or_equal(half(epsilon_0),n0)|~sQ17_spl),
% 0.15/0.48 inference(resolution,[status(thm)],[f487,f22])).
% 0.15/0.48 fof(f509,plain,(
% 0.15/0.48 sQ1_spl|~sQ17_spl),
% 0.15/0.48 inference(split_clause,[status(thm)],[f508,f68,f486])).
% 0.15/0.48 fof(f510,plain,(
% 0.15/0.48 $false),
% 0.15/0.48 inference(sat_refutation,[status(thm)],[f71,f84,f94,f245,f480,f489,f509])).
% 0.15/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.51 % Elapsed time: 0.077707 seconds
% 0.15/0.51 % CPU time: 0.246403 seconds
% 0.15/0.51 % Total memory used: 13.821 MB
% 0.15/0.51 % Net memory used: 13.496 MB
%------------------------------------------------------------------------------