TSTP Solution File: ANA002-4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ANA002-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 : Tue Apr 30 20:11:37 EDT 2024
% Result : Unsatisfiable 2.49s 0.69s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ANA002-4 : TPTP v8.1.2. Released v1.1.0.
% 0.03/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:22:19 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 2.49/0.69 % Refutation found
% 2.49/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.49/0.69 % SZS output start CNFRefutation for theBenchmark
% 2.49/0.69 fof(f1,axiom,(
% 2.49/0.69 (![X]: (less_than_or_equal(X,X) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f2,axiom,(
% 2.49/0.69 (![X,Y]: (( less_than_or_equal(X,Y)| less_than_or_equal(Y,X) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f3,axiom,(
% 2.49/0.69 (![X,Z,Y]: (( less_than_or_equal(X,Z)| ~ less_than_or_equal(X,Y)| ~ less_than_or_equal(Y,Z) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f4,axiom,(
% 2.49/0.69 (![X,Y]: (( ~ less_than_or_equal(X,q(Y,X))| less_than_or_equal(X,Y) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f5,axiom,(
% 2.49/0.69 (![X,Y]: (( ~ less_than_or_equal(q(X,Y),X)| less_than_or_equal(Y,X) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f6,axiom,(
% 2.49/0.69 (![X]: (( less_than_or_equal(f(X),n0)| ~ less_than_or_equal(X,h(X))| ~ less_than_or_equal(lower_bound,X)| ~ less_than_or_equal(X,upper_bound) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f7,axiom,(
% 2.49/0.69 (![X,Y]: (( less_than_or_equal(f(X),n0)| ~ less_than_or_equal(Y,X)| ~ less_than_or_equal(f(Y),n0)| less_than_or_equal(Y,h(X))| ~ less_than_or_equal(lower_bound,X)| ~ less_than_or_equal(X,upper_bound) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f8,axiom,(
% 2.49/0.69 (![X]: (( less_than_or_equal(n0,f(X))| ~ less_than_or_equal(k(X),X)| ~ less_than_or_equal(lower_bound,X)| ~ less_than_or_equal(X,upper_bound) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f9,axiom,(
% 2.49/0.69 (![X,Y]: (( less_than_or_equal(n0,f(X))| ~ less_than_or_equal(X,Y)| ~ less_than_or_equal(n0,f(Y))| less_than_or_equal(k(X),Y)| ~ less_than_or_equal(lower_bound,X)| ~ less_than_or_equal(X,upper_bound) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f10,axiom,(
% 2.49/0.69 (![X]: (( less_than_or_equal(X,l)| ~ less_than_or_equal(X,upper_bound)| ~ less_than_or_equal(f(X),n0) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f11,axiom,(
% 2.49/0.69 (![X]: (( less_than_or_equal(g(X),upper_bound)| less_than_or_equal(l,X) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f12,axiom,(
% 2.49/0.69 (![X]: (( less_than_or_equal(f(g(X)),n0)| less_than_or_equal(l,X) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f13,axiom,(
% 2.49/0.69 (![X]: (( ~ less_than_or_equal(g(X),X)| less_than_or_equal(l,X) ) ))),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f14,hypothesis,(
% 2.49/0.69 less_than_or_equal(lower_bound,upper_bound) ),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f15,hypothesis,(
% 2.49/0.69 less_than_or_equal(f(lower_bound),n0) ),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f16,hypothesis,(
% 2.49/0.69 less_than_or_equal(n0,f(upper_bound)) ),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f17,negated_conjecture,(
% 2.49/0.69 ( ~ less_than_or_equal(f(l),n0)| ~ less_than_or_equal(n0,f(l)) ) ),
% 2.49/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.49/0.69 fof(f18,plain,(
% 2.49/0.69 ![X0]: (less_than_or_equal(X0,X0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f1])).
% 2.49/0.69 fof(f19,plain,(
% 2.49/0.69 ![X0,X1]: (less_than_or_equal(X0,X1)|less_than_or_equal(X1,X0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f2])).
% 2.49/0.69 fof(f20,plain,(
% 2.49/0.69 ![Z,Y]: ((![X]: (less_than_or_equal(X,Z)|~less_than_or_equal(X,Y)))|~less_than_or_equal(Y,Z))),
% 2.49/0.69 inference(miniscoping,[status(esa)],[f3])).
% 2.49/0.69 fof(f21,plain,(
% 2.49/0.69 ![X0,X1,X2]: (less_than_or_equal(X0,X1)|~less_than_or_equal(X0,X2)|~less_than_or_equal(X2,X1))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f20])).
% 2.49/0.69 fof(f22,plain,(
% 2.49/0.69 ![X0,X1]: (~less_than_or_equal(X0,q(X1,X0))|less_than_or_equal(X0,X1))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f4])).
% 2.49/0.69 fof(f23,plain,(
% 2.49/0.69 ![X0,X1]: (~less_than_or_equal(q(X0,X1),X0)|less_than_or_equal(X1,X0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f5])).
% 2.49/0.69 fof(f24,plain,(
% 2.49/0.69 ![X0]: (less_than_or_equal(f(X0),n0)|~less_than_or_equal(X0,h(X0))|~less_than_or_equal(lower_bound,X0)|~less_than_or_equal(X0,upper_bound))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f6])).
% 2.49/0.69 fof(f25,plain,(
% 2.49/0.69 ![X]: (((![Y]: (((less_than_or_equal(f(X),n0)|~less_than_or_equal(Y,X))|~less_than_or_equal(f(Y),n0))|less_than_or_equal(Y,h(X))))|~less_than_or_equal(lower_bound,X))|~less_than_or_equal(X,upper_bound))),
% 2.49/0.69 inference(miniscoping,[status(esa)],[f7])).
% 2.49/0.69 fof(f26,plain,(
% 2.49/0.69 ![X0,X1]: (less_than_or_equal(f(X0),n0)|~less_than_or_equal(X1,X0)|~less_than_or_equal(f(X1),n0)|less_than_or_equal(X1,h(X0))|~less_than_or_equal(lower_bound,X0)|~less_than_or_equal(X0,upper_bound))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f25])).
% 2.49/0.69 fof(f27,plain,(
% 2.49/0.69 ![X0]: (less_than_or_equal(n0,f(X0))|~less_than_or_equal(k(X0),X0)|~less_than_or_equal(lower_bound,X0)|~less_than_or_equal(X0,upper_bound))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f8])).
% 2.49/0.69 fof(f28,plain,(
% 2.49/0.69 ![X]: (((![Y]: (((less_than_or_equal(n0,f(X))|~less_than_or_equal(X,Y))|~less_than_or_equal(n0,f(Y)))|less_than_or_equal(k(X),Y)))|~less_than_or_equal(lower_bound,X))|~less_than_or_equal(X,upper_bound))),
% 2.49/0.69 inference(miniscoping,[status(esa)],[f9])).
% 2.49/0.69 fof(f29,plain,(
% 2.49/0.69 ![X0,X1]: (less_than_or_equal(n0,f(X0))|~less_than_or_equal(X0,X1)|~less_than_or_equal(n0,f(X1))|less_than_or_equal(k(X0),X1)|~less_than_or_equal(lower_bound,X0)|~less_than_or_equal(X0,upper_bound))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f28])).
% 2.49/0.69 fof(f30,plain,(
% 2.49/0.69 ![X0]: (less_than_or_equal(X0,l)|~less_than_or_equal(X0,upper_bound)|~less_than_or_equal(f(X0),n0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f10])).
% 2.49/0.69 fof(f31,plain,(
% 2.49/0.69 ![X0]: (less_than_or_equal(g(X0),upper_bound)|less_than_or_equal(l,X0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f11])).
% 2.49/0.69 fof(f32,plain,(
% 2.49/0.69 ![X0]: (less_than_or_equal(f(g(X0)),n0)|less_than_or_equal(l,X0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f12])).
% 2.49/0.69 fof(f33,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(g(X0),X0)|less_than_or_equal(l,X0))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f13])).
% 2.49/0.69 fof(f34,plain,(
% 2.49/0.69 less_than_or_equal(lower_bound,upper_bound)),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f14])).
% 2.49/0.69 fof(f35,plain,(
% 2.49/0.69 less_than_or_equal(f(lower_bound),n0)),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f15])).
% 2.49/0.69 fof(f36,plain,(
% 2.49/0.69 less_than_or_equal(n0,f(upper_bound))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f16])).
% 2.49/0.69 fof(f37,plain,(
% 2.49/0.69 ~less_than_or_equal(f(l),n0)|~less_than_or_equal(n0,f(l))),
% 2.49/0.69 inference(cnf_transformation,[status(esa)],[f17])).
% 2.49/0.69 fof(f38,plain,(
% 2.49/0.69 spl0_0 <=> less_than_or_equal(f(l),n0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f40,plain,(
% 2.49/0.69 ~less_than_or_equal(f(l),n0)|spl0_0),
% 2.49/0.69 inference(component_clause,[status(thm)],[f38])).
% 2.49/0.69 fof(f41,plain,(
% 2.49/0.69 spl0_1 <=> less_than_or_equal(n0,f(l))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f43,plain,(
% 2.49/0.69 ~less_than_or_equal(n0,f(l))|spl0_1),
% 2.49/0.69 inference(component_clause,[status(thm)],[f41])).
% 2.49/0.69 fof(f44,plain,(
% 2.49/0.69 ~spl0_0|~spl0_1),
% 2.49/0.69 inference(split_clause,[status(thm)],[f37,f38,f41])).
% 2.49/0.69 fof(f45,plain,(
% 2.49/0.69 spl0_2 <=> ~less_than_or_equal(X0,l)|~less_than_or_equal(f(X0),n0)|less_than_or_equal(X0,h(l))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f46,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(X0,l)|~less_than_or_equal(f(X0),n0)|less_than_or_equal(X0,h(l))|~spl0_2)),
% 2.49/0.69 inference(component_clause,[status(thm)],[f45])).
% 2.49/0.69 fof(f48,plain,(
% 2.49/0.69 spl0_3 <=> less_than_or_equal(lower_bound,l)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f50,plain,(
% 2.49/0.69 ~less_than_or_equal(lower_bound,l)|spl0_3),
% 2.49/0.69 inference(component_clause,[status(thm)],[f48])).
% 2.49/0.69 fof(f51,plain,(
% 2.49/0.69 spl0_4 <=> less_than_or_equal(l,upper_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f53,plain,(
% 2.49/0.69 ~less_than_or_equal(l,upper_bound)|spl0_4),
% 2.49/0.69 inference(component_clause,[status(thm)],[f51])).
% 2.49/0.69 fof(f54,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(X0,l)|~less_than_or_equal(f(X0),n0)|less_than_or_equal(X0,h(l))|~less_than_or_equal(lower_bound,l)|~less_than_or_equal(l,upper_bound)|spl0_0)),
% 2.49/0.69 inference(resolution,[status(thm)],[f40,f26])).
% 2.49/0.69 fof(f55,plain,(
% 2.49/0.69 spl0_2|~spl0_3|~spl0_4|spl0_0),
% 2.49/0.69 inference(split_clause,[status(thm)],[f54,f45,f48,f51,f38])).
% 2.49/0.69 fof(f56,plain,(
% 2.49/0.69 spl0_5 <=> less_than_or_equal(l,h(l))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f58,plain,(
% 2.49/0.69 ~less_than_or_equal(l,h(l))|spl0_5),
% 2.49/0.69 inference(component_clause,[status(thm)],[f56])).
% 2.49/0.69 fof(f59,plain,(
% 2.49/0.69 ~less_than_or_equal(l,h(l))|~less_than_or_equal(lower_bound,l)|~less_than_or_equal(l,upper_bound)|spl0_0),
% 2.49/0.69 inference(resolution,[status(thm)],[f40,f24])).
% 2.49/0.69 fof(f60,plain,(
% 2.49/0.69 ~spl0_5|~spl0_3|~spl0_4|spl0_0),
% 2.49/0.69 inference(split_clause,[status(thm)],[f59,f56,f48,f51,f38])).
% 2.49/0.69 fof(f65,plain,(
% 2.49/0.69 spl0_6 <=> ~less_than_or_equal(l,X0)|~less_than_or_equal(n0,f(X0))|less_than_or_equal(k(l),X0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f66,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(l,X0)|~less_than_or_equal(n0,f(X0))|less_than_or_equal(k(l),X0)|~spl0_6)),
% 2.49/0.69 inference(component_clause,[status(thm)],[f65])).
% 2.49/0.69 fof(f68,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(l,X0)|~less_than_or_equal(n0,f(X0))|less_than_or_equal(k(l),X0)|~less_than_or_equal(lower_bound,l)|~less_than_or_equal(l,upper_bound)|spl0_1)),
% 2.49/0.69 inference(resolution,[status(thm)],[f43,f29])).
% 2.49/0.69 fof(f69,plain,(
% 2.49/0.69 spl0_6|~spl0_3|~spl0_4|spl0_1),
% 2.49/0.69 inference(split_clause,[status(thm)],[f68,f65,f48,f51,f41])).
% 2.49/0.69 fof(f70,plain,(
% 2.49/0.69 spl0_7 <=> less_than_or_equal(k(l),l)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f72,plain,(
% 2.49/0.69 ~less_than_or_equal(k(l),l)|spl0_7),
% 2.49/0.69 inference(component_clause,[status(thm)],[f70])).
% 2.49/0.69 fof(f73,plain,(
% 2.49/0.69 ~less_than_or_equal(k(l),l)|~less_than_or_equal(lower_bound,l)|~less_than_or_equal(l,upper_bound)|spl0_1),
% 2.49/0.69 inference(resolution,[status(thm)],[f43,f27])).
% 2.49/0.69 fof(f74,plain,(
% 2.49/0.69 ~spl0_7|~spl0_3|~spl0_4|spl0_1),
% 2.49/0.69 inference(split_clause,[status(thm)],[f73,f70,f48,f51,f41])).
% 2.49/0.69 fof(f79,plain,(
% 2.49/0.69 ~less_than_or_equal(g(upper_bound),upper_bound)|spl0_4),
% 2.49/0.69 inference(resolution,[status(thm)],[f53,f33])).
% 2.49/0.69 fof(f89,plain,(
% 2.49/0.69 spl0_8 <=> less_than_or_equal(k(l),upper_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f91,plain,(
% 2.49/0.69 ~less_than_or_equal(k(l),upper_bound)|spl0_8),
% 2.49/0.69 inference(component_clause,[status(thm)],[f89])).
% 2.49/0.69 fof(f97,plain,(
% 2.49/0.69 ~less_than_or_equal(q(l,k(l)),l)|spl0_7),
% 2.49/0.69 inference(resolution,[status(thm)],[f72,f23])).
% 2.49/0.69 fof(f97,plain,(
% 2.49/0.69 ~less_than_or_equal(q(l,k(l)),l)|spl0_7),
% 2.49/0.69 inference(resolution,[status(thm)],[f72,f23])).
% 2.49/0.69 fof(f98,plain,(
% 2.49/0.69 ~less_than_or_equal(k(l),q(l,k(l)))|spl0_7),
% 2.49/0.69 inference(resolution,[status(thm)],[f72,f22])).
% 2.49/0.69 fof(f109,plain,(
% 2.49/0.69 less_than_or_equal(l,upper_bound)|spl0_4),
% 2.49/0.69 inference(resolution,[status(thm)],[f79,f31])).
% 2.49/0.69 fof(f110,plain,(
% 2.49/0.69 $false|spl0_4),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f109,f53])).
% 2.49/0.69 fof(f111,plain,(
% 2.49/0.69 spl0_4),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f110])).
% 2.49/0.69 fof(f112,plain,(
% 2.49/0.69 spl0_10 <=> less_than_or_equal(lower_bound,upper_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f114,plain,(
% 2.49/0.69 ~less_than_or_equal(lower_bound,upper_bound)|spl0_10),
% 2.49/0.69 inference(component_clause,[status(thm)],[f112])).
% 2.49/0.69 fof(f115,plain,(
% 2.49/0.69 spl0_11 <=> less_than_or_equal(f(lower_bound),n0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f117,plain,(
% 2.49/0.69 ~less_than_or_equal(f(lower_bound),n0)|spl0_11),
% 2.49/0.69 inference(component_clause,[status(thm)],[f115])).
% 2.49/0.69 fof(f118,plain,(
% 2.49/0.69 ~less_than_or_equal(lower_bound,upper_bound)|~less_than_or_equal(f(lower_bound),n0)|spl0_3),
% 2.49/0.69 inference(resolution,[status(thm)],[f50,f30])).
% 2.49/0.69 fof(f119,plain,(
% 2.49/0.69 ~spl0_10|~spl0_11|spl0_3),
% 2.49/0.69 inference(split_clause,[status(thm)],[f118,f112,f115,f48])).
% 2.49/0.69 fof(f124,plain,(
% 2.49/0.69 $false|spl0_10),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f114,f34])).
% 2.49/0.69 fof(f125,plain,(
% 2.49/0.69 spl0_10),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f124])).
% 2.49/0.69 fof(f126,plain,(
% 2.49/0.69 $false|spl0_11),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f117,f35])).
% 2.49/0.69 fof(f127,plain,(
% 2.49/0.69 spl0_11),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f126])).
% 2.49/0.69 fof(f128,plain,(
% 2.49/0.69 ~less_than_or_equal(g(h(l)),h(l))|spl0_5),
% 2.49/0.69 inference(resolution,[status(thm)],[f58,f33])).
% 2.49/0.69 fof(f158,plain,(
% 2.49/0.69 spl0_15 <=> less_than_or_equal(n0,n0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f160,plain,(
% 2.49/0.69 ~less_than_or_equal(n0,n0)|spl0_15),
% 2.49/0.69 inference(component_clause,[status(thm)],[f158])).
% 2.49/0.69 fof(f198,plain,(
% 2.49/0.69 spl0_19 <=> less_than_or_equal(l,l)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f200,plain,(
% 2.49/0.69 ~less_than_or_equal(l,l)|spl0_19),
% 2.49/0.69 inference(component_clause,[status(thm)],[f198])).
% 2.49/0.69 fof(f203,plain,(
% 2.49/0.69 spl0_20 <=> less_than_or_equal(n0,f(upper_bound))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f205,plain,(
% 2.49/0.69 ~less_than_or_equal(n0,f(upper_bound))|spl0_20),
% 2.49/0.69 inference(component_clause,[status(thm)],[f203])).
% 2.49/0.69 fof(f206,plain,(
% 2.49/0.69 ~less_than_or_equal(l,upper_bound)|~less_than_or_equal(n0,f(upper_bound))|~spl0_6|spl0_8),
% 2.49/0.69 inference(resolution,[status(thm)],[f66,f91])).
% 2.49/0.69 fof(f207,plain,(
% 2.49/0.69 ~spl0_4|~spl0_20|~spl0_6|spl0_8),
% 2.49/0.69 inference(split_clause,[status(thm)],[f206,f51,f203,f65,f89])).
% 2.49/0.69 fof(f208,plain,(
% 2.49/0.69 $false|spl0_20),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f205,f36])).
% 2.49/0.69 fof(f209,plain,(
% 2.49/0.69 spl0_20),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f208])).
% 2.49/0.69 fof(f291,plain,(
% 2.49/0.69 $false|spl0_19),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f200,f18])).
% 2.49/0.69 fof(f292,plain,(
% 2.49/0.69 spl0_19),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f291])).
% 2.49/0.69 fof(f328,plain,(
% 2.49/0.69 spl0_31 <=> less_than_or_equal(q(l,k(l)),upper_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f330,plain,(
% 2.49/0.69 ~less_than_or_equal(q(l,k(l)),upper_bound)|spl0_31),
% 2.49/0.69 inference(component_clause,[status(thm)],[f328])).
% 2.49/0.69 fof(f331,plain,(
% 2.49/0.69 spl0_32 <=> less_than_or_equal(f(q(l,k(l))),n0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f333,plain,(
% 2.49/0.69 ~less_than_or_equal(f(q(l,k(l))),n0)|spl0_32),
% 2.49/0.69 inference(component_clause,[status(thm)],[f331])).
% 2.49/0.69 fof(f334,plain,(
% 2.49/0.69 ~less_than_or_equal(q(l,k(l)),upper_bound)|~less_than_or_equal(f(q(l,k(l))),n0)|spl0_7),
% 2.49/0.69 inference(resolution,[status(thm)],[f97,f30])).
% 2.49/0.69 fof(f335,plain,(
% 2.49/0.69 ~spl0_31|~spl0_32|spl0_7),
% 2.49/0.69 inference(split_clause,[status(thm)],[f334,f328,f331,f70])).
% 2.49/0.69 fof(f340,plain,(
% 2.49/0.69 spl0_33 <=> less_than_or_equal(l,q(l,k(l)))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f342,plain,(
% 2.49/0.69 ~less_than_or_equal(l,q(l,k(l)))|spl0_33),
% 2.49/0.69 inference(component_clause,[status(thm)],[f340])).
% 2.49/0.69 fof(f343,plain,(
% 2.49/0.69 spl0_34 <=> less_than_or_equal(n0,f(q(l,k(l))))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f346,plain,(
% 2.49/0.69 ~less_than_or_equal(l,q(l,k(l)))|~less_than_or_equal(n0,f(q(l,k(l))))|spl0_7|~spl0_6),
% 2.49/0.69 inference(resolution,[status(thm)],[f98,f66])).
% 2.49/0.69 fof(f347,plain,(
% 2.49/0.69 ~spl0_33|~spl0_34|spl0_7|~spl0_6),
% 2.49/0.69 inference(split_clause,[status(thm)],[f346,f340,f343,f70,f65])).
% 2.49/0.69 fof(f350,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(k(l),X0)|~less_than_or_equal(X0,q(l,k(l)))|spl0_7)),
% 2.49/0.69 inference(resolution,[status(thm)],[f98,f21])).
% 2.49/0.69 fof(f426,plain,(
% 2.49/0.69 spl0_39 <=> less_than_or_equal(upper_bound,upper_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f428,plain,(
% 2.49/0.69 ~less_than_or_equal(upper_bound,upper_bound)|spl0_39),
% 2.49/0.69 inference(component_clause,[status(thm)],[f426])).
% 2.49/0.69 fof(f437,plain,(
% 2.49/0.69 $false|spl0_39),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f428,f18])).
% 2.49/0.69 fof(f438,plain,(
% 2.49/0.69 spl0_39),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f437])).
% 2.49/0.69 fof(f651,plain,(
% 2.49/0.69 spl0_58 <=> ~less_than_or_equal(n0,X0)|~less_than_or_equal(X0,n0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f652,plain,(
% 2.49/0.69 ![X0]: (~less_than_or_equal(n0,X0)|~less_than_or_equal(X0,n0)|~spl0_58)),
% 2.49/0.69 inference(component_clause,[status(thm)],[f651])).
% 2.49/0.69 fof(f1266,plain,(
% 2.49/0.69 $false|spl0_15),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f160,f18])).
% 2.49/0.69 fof(f1267,plain,(
% 2.49/0.69 spl0_15),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f1266])).
% 2.49/0.69 fof(f1316,plain,(
% 2.49/0.69 spl0_107 <=> less_than_or_equal(q(l,k(l)),l)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f1318,plain,(
% 2.49/0.69 ~less_than_or_equal(q(l,k(l)),l)|spl0_107),
% 2.49/0.69 inference(component_clause,[status(thm)],[f1316])).
% 2.49/0.69 fof(f1334,plain,(
% 2.49/0.69 less_than_or_equal(upper_bound,q(l,k(l)))|spl0_31),
% 2.49/0.69 inference(resolution,[status(thm)],[f330,f19])).
% 2.49/0.69 fof(f1394,plain,(
% 2.49/0.69 ~less_than_or_equal(n0,n0)|~spl0_58),
% 2.49/0.69 inference(resolution,[status(thm)],[f652,f18])).
% 2.49/0.69 fof(f1395,plain,(
% 2.49/0.69 ~spl0_15|~spl0_58),
% 2.49/0.69 inference(split_clause,[status(thm)],[f1394,f158,f651])).
% 2.49/0.69 fof(f1867,plain,(
% 2.49/0.69 spl0_138 <=> less_than_or_equal(g(h(l)),l)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f1869,plain,(
% 2.49/0.69 ~less_than_or_equal(g(h(l)),l)|spl0_138),
% 2.49/0.69 inference(component_clause,[status(thm)],[f1867])).
% 2.49/0.69 fof(f1870,plain,(
% 2.49/0.69 spl0_139 <=> less_than_or_equal(f(g(h(l))),n0)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f1872,plain,(
% 2.49/0.69 ~less_than_or_equal(f(g(h(l))),n0)|spl0_139),
% 2.49/0.69 inference(component_clause,[status(thm)],[f1870])).
% 2.49/0.69 fof(f1873,plain,(
% 2.49/0.69 ~less_than_or_equal(g(h(l)),l)|~less_than_or_equal(f(g(h(l))),n0)|spl0_5|~spl0_2),
% 2.49/0.69 inference(resolution,[status(thm)],[f128,f46])).
% 2.49/0.69 fof(f1874,plain,(
% 2.49/0.69 ~spl0_138|~spl0_139|spl0_5|~spl0_2),
% 2.49/0.69 inference(split_clause,[status(thm)],[f1873,f1867,f1870,f56,f45])).
% 2.49/0.69 fof(f2007,plain,(
% 2.49/0.69 spl0_142 <=> less_than_or_equal(g(h(l)),upper_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f2009,plain,(
% 2.49/0.69 ~less_than_or_equal(g(h(l)),upper_bound)|spl0_142),
% 2.49/0.69 inference(component_clause,[status(thm)],[f2007])).
% 2.49/0.69 fof(f2010,plain,(
% 2.49/0.69 ~less_than_or_equal(g(h(l)),upper_bound)|~less_than_or_equal(f(g(h(l))),n0)|spl0_138),
% 2.49/0.69 inference(resolution,[status(thm)],[f1869,f30])).
% 2.49/0.69 fof(f2011,plain,(
% 2.49/0.69 ~spl0_142|~spl0_139|spl0_138),
% 2.49/0.69 inference(split_clause,[status(thm)],[f2010,f2007,f1870,f1867])).
% 2.49/0.69 fof(f2069,plain,(
% 2.49/0.69 spl0_147 <=> less_than_or_equal(lower_bound,lower_bound)),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f2071,plain,(
% 2.49/0.69 ~less_than_or_equal(lower_bound,lower_bound)|spl0_147),
% 2.49/0.69 inference(component_clause,[status(thm)],[f2069])).
% 2.49/0.69 fof(f2083,plain,(
% 2.49/0.69 $false|spl0_147),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f2071,f18])).
% 2.49/0.69 fof(f2084,plain,(
% 2.49/0.69 spl0_147),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f2083])).
% 2.49/0.69 fof(f2089,plain,(
% 2.49/0.69 less_than_or_equal(l,h(l))|spl0_142),
% 2.49/0.69 inference(resolution,[status(thm)],[f2009,f31])).
% 2.49/0.69 fof(f2090,plain,(
% 2.49/0.69 $false|spl0_5|spl0_142),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f2089,f58])).
% 2.49/0.69 fof(f2091,plain,(
% 2.49/0.69 spl0_5|spl0_142),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f2090])).
% 2.49/0.69 fof(f2546,plain,(
% 2.49/0.69 spl0_187 <=> less_than_or_equal(k(l),k(l))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f2548,plain,(
% 2.49/0.69 ~less_than_or_equal(k(l),k(l))|spl0_187),
% 2.49/0.69 inference(component_clause,[status(thm)],[f2546])).
% 2.49/0.69 fof(f2551,plain,(
% 2.49/0.69 $false|spl0_187),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f2548,f18])).
% 2.49/0.69 fof(f2552,plain,(
% 2.49/0.69 spl0_187),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f2551])).
% 2.49/0.69 fof(f2750,plain,(
% 2.49/0.69 spl0_202 <=> less_than_or_equal(f(l),f(l))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f2752,plain,(
% 2.49/0.69 ~less_than_or_equal(f(l),f(l))|spl0_202),
% 2.49/0.69 inference(component_clause,[status(thm)],[f2750])).
% 2.49/0.69 fof(f2784,plain,(
% 2.49/0.69 $false|spl0_202),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f2752,f18])).
% 2.49/0.69 fof(f2785,plain,(
% 2.49/0.69 spl0_202),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f2784])).
% 2.49/0.69 fof(f2885,plain,(
% 2.49/0.69 less_than_or_equal(l,q(l,k(l)))|spl0_107),
% 2.49/0.69 inference(resolution,[status(thm)],[f1318,f19])).
% 2.49/0.69 fof(f2886,plain,(
% 2.49/0.69 $false|spl0_33|spl0_107),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f2885,f342])).
% 2.49/0.69 fof(f2887,plain,(
% 2.49/0.69 spl0_33|spl0_107),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f2886])).
% 2.49/0.69 fof(f3013,plain,(
% 2.49/0.69 spl0_226 <=> less_than_or_equal(h(l),h(l))),
% 2.49/0.69 introduced(split_symbol_definition)).
% 2.49/0.69 fof(f3015,plain,(
% 2.49/0.69 ~less_than_or_equal(h(l),h(l))|spl0_226),
% 2.49/0.69 inference(component_clause,[status(thm)],[f3013])).
% 2.49/0.69 fof(f3025,plain,(
% 2.49/0.69 $false|spl0_226),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f3015,f18])).
% 2.49/0.69 fof(f3026,plain,(
% 2.49/0.69 spl0_226),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f3025])).
% 2.49/0.69 fof(f3177,plain,(
% 2.49/0.69 less_than_or_equal(l,h(l))|spl0_139),
% 2.49/0.69 inference(resolution,[status(thm)],[f1872,f32])).
% 2.49/0.69 fof(f3178,plain,(
% 2.49/0.69 $false|spl0_5|spl0_139),
% 2.49/0.69 inference(forward_subsumption_resolution,[status(thm)],[f3177,f58])).
% 2.49/0.69 fof(f3179,plain,(
% 2.49/0.69 spl0_5|spl0_139),
% 2.49/0.69 inference(contradiction_clause,[status(thm)],[f3178])).
% 2.49/0.69 fof(f3210,plain,(
% 2.49/0.69 ~spl0_107|spl0_7),
% 2.49/0.69 inference(split_clause,[status(thm)],[f97,f1316,f70])).
% 2.49/0.69 fof(f4453,plain,(
% 2.49/0.69 less_than_or_equal(n0,f(q(l,k(l))))|spl0_32),
% 2.49/0.69 inference(resolution,[status(thm)],[f333,f19])).
% 2.49/0.70 fof(f4454,plain,(
% 2.49/0.70 spl0_34|spl0_32),
% 2.49/0.70 inference(split_clause,[status(thm)],[f4453,f343,f331])).
% 2.49/0.70 fof(f4696,plain,(
% 2.49/0.70 ~less_than_or_equal(k(l),upper_bound)|spl0_7|spl0_31),
% 2.49/0.70 inference(resolution,[status(thm)],[f350,f1334])).
% 2.49/0.70 fof(f4697,plain,(
% 2.49/0.70 ~spl0_8|spl0_7|spl0_31),
% 2.49/0.70 inference(split_clause,[status(thm)],[f4696,f89,f70,f328])).
% 2.49/0.70 fof(f4730,plain,(
% 2.49/0.70 $false),
% 2.49/0.70 inference(sat_refutation,[status(thm)],[f44,f55,f60,f69,f74,f111,f119,f125,f127,f207,f209,f292,f335,f347,f438,f1267,f1395,f1874,f2011,f2084,f2091,f2552,f2785,f2887,f3026,f3179,f3210,f4454,f4697])).
% 2.49/0.70 % SZS output end CNFRefutation for theBenchmark.p
% 2.49/0.70 % Elapsed time: 0.337098 seconds
% 2.49/0.70 % CPU time: 2.593035 seconds
% 2.49/0.70 % Total memory used: 30.557 MB
% 2.49/0.70 % Net memory used: 27.291 MB
%------------------------------------------------------------------------------