TSTP Solution File: ANA003-4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:01:22 EDT 2023
% Result : Unsatisfiable 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue May 30 09:49:32 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.34 fof(f1,axiom,(
% 0.11/0.34 (![Z,X,Y]: (( ~ less_or_equal(Z,minimum(X,Y))| less_or_equal(Z,X) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f2,axiom,(
% 0.11/0.34 (![Z,X,Y]: (( ~ less_or_equal(Z,minimum(X,Y))| less_or_equal(Z,Y) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f3,axiom,(
% 0.11/0.34 (![X,Y]: (( less_or_equal(X,n0)| less_or_equal(Y,n0)| ~ less_or_equal(minimum(X,Y),n0) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f4,axiom,(
% 0.11/0.34 (![X,Z,Y]: (( ~ less_or_equal(X,half(Z))| ~ less_or_equal(Y,half(Z))| less_or_equal(add(X,Y),Z) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f5,axiom,(
% 0.11/0.34 (![X]: (( less_or_equal(X,n0)| ~ less_or_equal(half(X),n0) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f6,hypothesis,(
% 0.11/0.34 (![Epsilon]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(delta_1(Epsilon),n0) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f7,hypothesis,(
% 0.11/0.34 (![Epsilon]: (( less_or_equal(Epsilon,n0)| ~ less_or_equal(delta_2(Epsilon),n0) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f8,hypothesis,(
% 0.11/0.34 (![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) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f9,hypothesis,(
% 0.11/0.34 (![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) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f10,hypothesis,(
% 0.11/0.34 ~ less_or_equal(epsilon_0,n0) ),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f11,hypothesis,(
% 0.11/0.34 (![Delta]: (( less_or_equal(Delta,n0)| less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f12,negated_conjecture,(
% 0.11/0.34 (![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) ) ))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.34 fof(f13,plain,(
% 0.11/0.34 ![Z,X]: ((![Y]: ~less_or_equal(Z,minimum(X,Y)))|less_or_equal(Z,X))),
% 0.11/0.34 inference(miniscoping,[status(esa)],[f1])).
% 0.11/0.34 fof(f14,plain,(
% 0.11/0.34 ![X0,X1,X2]: (~less_or_equal(X0,minimum(X1,X2))|less_or_equal(X0,X1))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f13])).
% 0.11/0.34 fof(f15,plain,(
% 0.11/0.34 ![Z,Y]: ((![X]: ~less_or_equal(Z,minimum(X,Y)))|less_or_equal(Z,Y))),
% 0.11/0.34 inference(miniscoping,[status(esa)],[f2])).
% 0.11/0.34 fof(f16,plain,(
% 0.11/0.34 ![X0,X1,X2]: (~less_or_equal(X0,minimum(X1,X2))|less_or_equal(X0,X2))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f15])).
% 0.11/0.34 fof(f17,plain,(
% 0.11/0.34 ![X0,X1]: (less_or_equal(X0,n0)|less_or_equal(X1,n0)|~less_or_equal(minimum(X0,X1),n0))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f3])).
% 0.11/0.34 fof(f18,plain,(
% 0.11/0.34 ![X0,X1,X2]: (~less_or_equal(X0,half(X1))|~less_or_equal(X2,half(X1))|less_or_equal(add(X0,X2),X1))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f4])).
% 0.11/0.34 fof(f19,plain,(
% 0.11/0.34 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(half(X0),n0))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f5])).
% 0.11/0.34 fof(f20,plain,(
% 0.11/0.34 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(delta_1(X0),n0))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f6])).
% 0.11/0.34 fof(f21,plain,(
% 0.11/0.34 ![X0]: (less_or_equal(X0,n0)|~less_or_equal(delta_2(X0),n0))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f7])).
% 0.11/0.34 fof(f22,plain,(
% 0.11/0.34 ![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))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f8])).
% 0.11/0.34 fof(f23,plain,(
% 0.11/0.34 ![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))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f9])).
% 0.11/0.34 fof(f24,plain,(
% 0.11/0.34 ~less_or_equal(epsilon_0,n0)),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f10])).
% 0.11/0.34 fof(f25,plain,(
% 0.11/0.34 ![X0]: (less_or_equal(X0,n0)|less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f11])).
% 0.11/0.34 fof(f26,plain,(
% 0.11/0.34 ![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))),
% 0.11/0.34 inference(cnf_transformation,[status(esa)],[f12])).
% 0.11/0.34 fof(f27,plain,(
% 0.11/0.34 ![X0,X1]: (less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0)|less_or_equal(minimum(X0,X1),n0))),
% 0.11/0.34 inference(resolution,[status(thm)],[f14,f25])).
% 0.11/0.34 fof(f28,plain,(
% 0.11/0.34 ![X0,X1]: (less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1)|less_or_equal(minimum(X0,X1),n0))),
% 0.11/0.34 inference(resolution,[status(thm)],[f16,f25])).
% 0.11/0.34 fof(f29,plain,(
% 0.11/0.34 ![X0,X1]: (less_or_equal(X0,n0)|less_or_equal(X1,n0)|less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1))),
% 0.11/0.34 inference(resolution,[status(thm)],[f17,f28])).
% 0.11/0.34 fof(f30,plain,(
% 0.11/0.34 ![X0,X1]: (less_or_equal(X0,n0)|less_or_equal(X1,n0)|less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0))),
% 0.11/0.34 inference(resolution,[status(thm)],[f17,f27])).
% 0.11/0.34 fof(f41,plain,(
% 0.11/0.34 ![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))),
% 0.11/0.34 inference(resolution,[status(thm)],[f18,f26])).
% 0.11/0.34 fof(f81,plain,(
% 0.11/0.34 spl0_0 <=> ~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)))),
% 0.11/0.34 introduced(split_symbol_definition)).
% 0.11/0.34 fof(f82,plain,(
% 0.11/0.34 ![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)))|~spl0_0)),
% 0.11/0.34 inference(component_clause,[status(thm)],[f81])).
% 0.11/0.34 fof(f84,plain,(
% 0.11/0.34 spl0_1 <=> less_or_equal(half(epsilon_0),n0)),
% 0.11/0.34 introduced(split_symbol_definition)).
% 0.11/0.34 fof(f85,plain,(
% 0.11/0.34 less_or_equal(half(epsilon_0),n0)|~spl0_1),
% 0.11/0.34 inference(component_clause,[status(thm)],[f84])).
% 0.11/0.34 fof(f87,plain,(
% 0.11/0.34 ![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))))),
% 0.11/0.34 inference(resolution,[status(thm)],[f41,f23])).
% 0.11/0.34 fof(f88,plain,(
% 0.11/0.34 spl0_0|spl0_1),
% 0.11/0.34 inference(split_clause,[status(thm)],[f87,f81,f84])).
% 0.11/0.34 fof(f91,plain,(
% 0.11/0.34 spl0_2 <=> 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)))),
% 0.11/0.34 introduced(split_symbol_definition)).
% 0.11/0.34 fof(f92,plain,(
% 0.11/0.34 ![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)))|~spl0_2)),
% 0.11/0.34 inference(component_clause,[status(thm)],[f91])).
% 0.11/0.34 fof(f94,plain,(
% 0.11/0.34 ![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)))|~spl0_0)),
% 0.11/0.34 inference(resolution,[status(thm)],[f82,f22])).
% 0.11/0.34 fof(f95,plain,(
% 0.11/0.34 spl0_2|spl0_1|~spl0_0),
% 0.11/0.34 inference(split_clause,[status(thm)],[f94,f91,f84,f81])).
% 0.11/0.34 fof(f96,plain,(
% 0.11/0.34 less_or_equal(epsilon_0,n0)|~spl0_1),
% 0.11/0.34 inference(resolution,[status(thm)],[f85,f19])).
% 0.11/0.34 fof(f97,plain,(
% 0.11/0.34 $false|~spl0_1),
% 0.11/0.34 inference(forward_subsumption_resolution,[status(thm)],[f96,f24])).
% 0.11/0.34 fof(f98,plain,(
% 0.11/0.34 ~spl0_1),
% 0.11/0.34 inference(contradiction_clause,[status(thm)],[f97])).
% 0.11/0.34 fof(f99,plain,(
% 0.11/0.34 ![X0,X1]: (~less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),delta_2(half(epsilon_0)))|~less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),delta_1(half(epsilon_0)))|less_or_equal(X0,n0)|less_or_equal(X1,n0)|~spl0_2)),
% 0.11/0.34 inference(resolution,[status(thm)],[f92,f17])).
% 0.11/0.34 fof(f124,plain,(
% 0.11/0.34 spl0_8 <=> less_or_equal(delta_2(half(epsilon_0)),n0)),
% 0.11/0.34 introduced(split_symbol_definition)).
% 0.11/0.34 fof(f125,plain,(
% 0.11/0.34 less_or_equal(delta_2(half(epsilon_0)),n0)|~spl0_8),
% 0.11/0.34 inference(component_clause,[status(thm)],[f124])).
% 0.11/0.34 fof(f144,plain,(
% 0.11/0.34 spl0_12 <=> ~less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),X0)),negate(a_real_number))),delta_1(half(epsilon_0)))|less_or_equal(X0,n0)|less_or_equal(X0,n0)),
% 0.11/0.34 introduced(split_symbol_definition)).
% 0.11/0.34 fof(f145,plain,(
% 0.11/0.34 ![X0]: (~less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),X0)),negate(a_real_number))),delta_1(half(epsilon_0)))|less_or_equal(X0,n0)|less_or_equal(X0,n0)|~spl0_12)),
% 0.11/0.34 inference(component_clause,[status(thm)],[f144])).
% 0.11/0.34 fof(f147,plain,(
% 0.11/0.34 ![X0]: (~less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),X0)),negate(a_real_number))),delta_1(half(epsilon_0)))|less_or_equal(delta_2(half(epsilon_0)),n0)|less_or_equal(X0,n0)|less_or_equal(delta_2(half(epsilon_0)),n0)|less_or_equal(X0,n0)|~spl0_2)),
% 0.11/0.34 inference(resolution,[status(thm)],[f99,f30])).
% 0.11/0.34 fof(f148,plain,(
% 0.11/0.34 spl0_12|spl0_8|~spl0_2),
% 0.11/0.34 inference(split_clause,[status(thm)],[f147,f144,f124,f91])).
% 0.11/0.34 fof(f154,plain,(
% 0.11/0.34 less_or_equal(half(epsilon_0),n0)|~spl0_8),
% 0.11/0.34 inference(resolution,[status(thm)],[f125,f21])).
% 0.11/0.34 fof(f155,plain,(
% 0.11/0.34 spl0_1|~spl0_8),
% 0.11/0.34 inference(split_clause,[status(thm)],[f154,f84,f124])).
% 0.11/0.34 fof(f160,plain,(
% 0.11/0.34 ![X0]: (~less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),X0)),negate(a_real_number))),delta_1(half(epsilon_0)))|less_or_equal(X0,n0)|~spl0_12)),
% 0.11/0.34 inference(duplicate_literals_removal,[status(esa)],[f145])).
% 0.11/0.34 fof(f187,plain,(
% 0.11/0.34 spl0_19 <=> less_or_equal(delta_1(half(epsilon_0)),n0)),
% 0.11/0.34 introduced(split_symbol_definition)).
% 0.11/0.34 fof(f188,plain,(
% 0.11/0.34 less_or_equal(delta_1(half(epsilon_0)),n0)|~spl0_19),
% 0.11/0.34 inference(component_clause,[status(thm)],[f187])).
% 0.11/0.34 fof(f197,plain,(
% 0.11/0.34 less_or_equal(delta_1(half(epsilon_0)),n0)|less_or_equal(delta_2(half(epsilon_0)),n0)|less_or_equal(delta_1(half(epsilon_0)),n0)|~spl0_12),
% 0.11/0.34 inference(resolution,[status(thm)],[f160,f29])).
% 0.11/0.34 fof(f198,plain,(
% 0.11/0.34 spl0_19|spl0_8|~spl0_12),
% 0.11/0.34 inference(split_clause,[status(thm)],[f197,f187,f124,f144])).
% 0.11/0.34 fof(f199,plain,(
% 0.11/0.34 less_or_equal(half(epsilon_0),n0)|~spl0_19),
% 0.11/0.34 inference(resolution,[status(thm)],[f188,f20])).
% 0.11/0.34 fof(f200,plain,(
% 0.11/0.34 spl0_1|~spl0_19),
% 0.11/0.34 inference(split_clause,[status(thm)],[f199,f84,f187])).
% 0.11/0.34 fof(f201,plain,(
% 0.11/0.34 $false),
% 0.11/0.34 inference(sat_refutation,[status(thm)],[f88,f95,f98,f148,f155,f198,f200])).
% 0.11/0.34 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.56 % Elapsed time: 0.016717 seconds
% 0.16/0.56 % CPU time: 0.018876 seconds
% 0.16/0.56 % Memory used: 933.933 KB
%------------------------------------------------------------------------------