%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 06:51:04 AM UTC 2026
% Result : Unsatisfiable 84.72s 11.26s
% Output : CNFRefutation 84.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 117 ( 27 unt; 0 def)
% Number of atoms : 328 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 361 ( 150 ~; 211 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(totality_of_less,axiom,
! [VAR_0,VAR_1] :
( less_than_or_equal(VAR_1,VAR_0)
| less_than_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',totality_of_less) ).
cnf(c_2,plain,
( less_than_or_equal(B,A)
| less_than_or_equal(A,B) ),
inference(clausify,[status(thm)],[totality_of_less]) ).
fof(transitivity_of_less,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_than_or_equal(VAR_2,VAR_1)
| ~ less_than_or_equal(VAR_0,VAR_2)
| less_than_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less) ).
cnf(c_3,plain,
( ~ less_than_or_equal(C,B)
| ~ less_than_or_equal(A,C)
| less_than_or_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less]) ).
fof(interpolation1,axiom,
! [VAR_0,VAR_1] :
( less_than_or_equal(VAR_0,VAR_1)
| ~ less_than_or_equal(VAR_0,q(VAR_1,VAR_0)) ),
file('theBenchmark.p',interpolation1) ).
cnf(c_4,plain,
( less_than_or_equal(A,B)
| ~ less_than_or_equal(A,q(B,A)) ),
inference(clausify,[status(thm)],[interpolation1]) ).
fof(interpolation2,axiom,
! [VAR_0,VAR_1] :
( less_than_or_equal(VAR_1,VAR_0)
| ~ less_than_or_equal(q(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',interpolation2) ).
cnf(c_5,plain,
( less_than_or_equal(B,A)
| ~ less_than_or_equal(q(A,B),A) ),
inference(clausify,[status(thm)],[interpolation2]) ).
fof(continuity1,axiom,
! [VAR_0] :
( ~ less_than_or_equal(VAR_0,upper_bound)
| ~ less_than_or_equal(lower_bound,VAR_0)
| ~ less_than_or_equal(VAR_0,h(VAR_0))
| less_than_or_equal(f(VAR_0),n0) ),
file('theBenchmark.p',continuity1) ).
cnf(c_6,plain,
( ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| ~ less_than_or_equal(A,h(A))
| less_than_or_equal(f(A),n0) ),
inference(clausify,[status(thm)],[continuity1]) ).
fof(continuity2,axiom,
! [VAR_0,VAR_1] :
( ~ less_than_or_equal(VAR_0,upper_bound)
| ~ less_than_or_equal(lower_bound,VAR_0)
| less_than_or_equal(VAR_1,h(VAR_0))
| ~ less_than_or_equal(f(VAR_1),n0)
| ~ less_than_or_equal(VAR_1,VAR_0)
| less_than_or_equal(f(VAR_0),n0) ),
file('theBenchmark.p',continuity2) ).
cnf(c_7,plain,
( ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| less_than_or_equal(B,h(A))
| ~ less_than_or_equal(f(B),n0)
| ~ less_than_or_equal(B,A)
| less_than_or_equal(f(A),n0) ),
inference(clausify,[status(thm)],[continuity2]) ).
fof(continuity3,axiom,
! [VAR_0] :
( ~ less_than_or_equal(VAR_0,upper_bound)
| ~ less_than_or_equal(lower_bound,VAR_0)
| ~ less_than_or_equal(k(VAR_0),VAR_0)
| less_than_or_equal(n0,f(VAR_0)) ),
file('theBenchmark.p',continuity3) ).
cnf(c_8,plain,
( ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| ~ less_than_or_equal(k(A),A)
| less_than_or_equal(n0,f(A)) ),
inference(clausify,[status(thm)],[continuity3]) ).
fof(continuity4,axiom,
! [VAR_0,VAR_1] :
( ~ less_than_or_equal(VAR_0,upper_bound)
| ~ less_than_or_equal(lower_bound,VAR_0)
| less_than_or_equal(k(VAR_0),VAR_1)
| ~ less_than_or_equal(n0,f(VAR_1))
| ~ less_than_or_equal(VAR_0,VAR_1)
| less_than_or_equal(n0,f(VAR_0)) ),
file('theBenchmark.p',continuity4) ).
cnf(c_9,plain,
( ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| less_than_or_equal(k(A),B)
| ~ less_than_or_equal(n0,f(B))
| ~ less_than_or_equal(A,B)
| less_than_or_equal(n0,f(A)) ),
inference(clausify,[status(thm)],[continuity4]) ).
fof(crossover1,axiom,
! [VAR_0] :
( ~ less_than_or_equal(f(VAR_0),n0)
| ~ less_than_or_equal(VAR_0,upper_bound)
| less_than_or_equal(VAR_0,l) ),
file('theBenchmark.p',crossover1) ).
cnf(c_10,plain,
( ~ less_than_or_equal(f(A),n0)
| ~ less_than_or_equal(A,upper_bound)
| less_than_or_equal(A,l) ),
inference(clausify,[status(thm)],[crossover1]) ).
fof(crossover2_and_g_function1,axiom,
! [VAR_0] :
( less_than_or_equal(l,VAR_0)
| less_than_or_equal(g(VAR_0),upper_bound) ),
file('theBenchmark.p',crossover2_and_g_function1) ).
cnf(c_11,plain,
( less_than_or_equal(l,A)
| less_than_or_equal(g(A),upper_bound) ),
inference(clausify,[status(thm)],[crossover2_and_g_function1]) ).
fof(crossover3_and_g_function2,axiom,
! [VAR_0] :
( less_than_or_equal(l,VAR_0)
| less_than_or_equal(f(g(VAR_0)),n0) ),
file('theBenchmark.p',crossover3_and_g_function2) ).
cnf(c_12,plain,
( less_than_or_equal(l,A)
| less_than_or_equal(f(g(A)),n0) ),
inference(clausify,[status(thm)],[crossover3_and_g_function2]) ).
fof(crossover4_and_g_function3,axiom,
! [VAR_0] :
( less_than_or_equal(l,VAR_0)
| ~ less_than_or_equal(g(VAR_0),VAR_0) ),
file('theBenchmark.p',crossover4_and_g_function3) ).
cnf(c_13,plain,
( less_than_or_equal(l,A)
| ~ less_than_or_equal(g(A),A) ),
inference(clausify,[status(thm)],[crossover4_and_g_function3]) ).
fof(the_interval,axiom,
less_than_or_equal(lower_bound,upper_bound),
file('theBenchmark.p',the_interval) ).
cnf(c_14,plain,
less_than_or_equal(lower_bound,upper_bound),
inference(clausify,[status(thm)],[the_interval]) ).
fof(lower_mapping,axiom,
less_than_or_equal(f(lower_bound),n0),
file('theBenchmark.p',lower_mapping) ).
cnf(c_15,plain,
less_than_or_equal(f(lower_bound),n0),
inference(clausify,[status(thm)],[lower_mapping]) ).
fof(upper_mapping,axiom,
less_than_or_equal(n0,f(upper_bound)),
file('theBenchmark.p',upper_mapping) ).
cnf(c_16,plain,
less_than_or_equal(n0,f(upper_bound)),
inference(clausify,[status(thm)],[upper_mapping]) ).
fof(prove_there_is_x_which_crosses,axiom,
( ~ less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(f(l),n0) ),
file('theBenchmark.p',prove_there_is_x_which_crosses) ).
cnf(c_17,plain,
( ~ less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(f(l),n0) ),
inference(clausify,[status(thm)],[prove_there_is_x_which_crosses]) ).
cnf(c_20,plain,
( less_than_or_equal(C,A)
| ~ less_than_or_equal(C,B)
| less_than_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_24,plain,
( less_than_or_equal(A,B)
| ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| less_than_or_equal(B,h(A))
| ~ less_than_or_equal(f(B),n0)
| less_than_or_equal(f(A),n0) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_25,plain,
( less_than_or_equal(n0,f(B))
| ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| less_than_or_equal(B,h(A))
| ~ less_than_or_equal(B,A)
| less_than_or_equal(f(A),n0) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_27,plain,
( less_than_or_equal(A,k(A))
| ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| less_than_or_equal(n0,f(A)) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_29,plain,
( less_than_or_equal(f(B),n0)
| ~ less_than_or_equal(A,upper_bound)
| ~ less_than_or_equal(lower_bound,A)
| less_than_or_equal(k(A),B)
| ~ less_than_or_equal(A,B)
| less_than_or_equal(n0,f(A)) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_33,plain,
( less_than_or_equal(n0,f(A))
| ~ less_than_or_equal(A,upper_bound)
| less_than_or_equal(A,l) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_38,plain,
( ~ less_than_or_equal(g(A),upper_bound)
| less_than_or_equal(g(A),l)
| less_than_or_equal(l,A) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_39,plain,
( ~ less_than_or_equal(B,upper_bound)
| ~ less_than_or_equal(lower_bound,B)
| less_than_or_equal(g(A),h(B))
| ~ less_than_or_equal(g(A),B)
| less_than_or_equal(f(B),n0)
| less_than_or_equal(l,A) ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_4873,plain,
( less_than_or_equal(l,upper_bound)
| less_than_or_equal(l,upper_bound) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_43,plain,
less_than_or_equal(l,upper_bound),
inference(copy,[status(thm)],[c_4873]) ).
cnf(c_4874,plain,
( ~ less_than_or_equal(lower_bound,upper_bound)
| less_than_or_equal(lower_bound,l) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_50,plain,
less_than_or_equal(lower_bound,l),
inference(resolve,[status(thm)],[c_14,c_4874]) ).
cnf(c_65,plain,
( less_than_or_equal(B,C)
| less_than_or_equal(C,A)
| less_than_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_20,c_2]) ).
cnf(c_4875,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(n0,f(upper_bound))
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_43,c_9]) ).
cnf(c_4876,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_16,c_4875]) ).
cnf(c_4877,plain,
( ~ less_than_or_equal(l,upper_bound)
| less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_50,c_4876]) ).
cnf(c_71,plain,
( less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_43,c_4877]) ).
cnf(c_75,plain,
( less_than_or_equal(lower_bound,A)
| less_than_or_equal(A,l) ),
inference(resolve,[status(thm)],[c_50,c_20]) ).
cnf(c_80,plain,
( ~ less_than_or_equal(A,lower_bound)
| less_than_or_equal(A,l) ),
inference(resolve,[status(thm)],[c_50,c_3]) ).
cnf(c_4878,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(n0,f(l))
| less_than_or_equal(lower_bound,k(l)) ),
inference(resolve,[status(thm)],[c_75,c_8]) ).
cnf(c_4879,plain,
( ~ less_than_or_equal(l,upper_bound)
| less_than_or_equal(n0,f(l))
| less_than_or_equal(lower_bound,k(l)) ),
inference(resolve,[status(thm)],[c_50,c_4878]) ).
cnf(c_105,plain,
( less_than_or_equal(n0,f(l))
| less_than_or_equal(lower_bound,k(l)) ),
inference(resolve,[status(thm)],[c_43,c_4879]) ).
cnf(c_4880,plain,
( less_than_or_equal(l,k(l))
| ~ less_than_or_equal(l,upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_27,c_50]) ).
cnf(c_164,plain,
( less_than_or_equal(l,k(l))
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_43,c_4880]) ).
cnf(c_182,plain,
( less_than_or_equal(B,C)
| ~ less_than_or_equal(B,upper_bound)
| less_than_or_equal(C,h(B))
| ~ less_than_or_equal(f(C),n0)
| less_than_or_equal(f(B),n0)
| less_than_or_equal(B,A)
| less_than_or_equal(A,lower_bound) ),
inference(resolve,[status(thm)],[c_65,c_24]) ).
cnf(c_451,plain,
( less_than_or_equal(k(l),A)
| less_than_or_equal(A,upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_71,c_20]) ).
cnf(c_4881,plain,
( less_than_or_equal(l,A)
| less_than_or_equal(g(A),l)
| less_than_or_equal(l,A) ),
inference(resolve,[status(thm)],[c_38,c_11]) ).
cnf(c_526,plain,
( less_than_or_equal(g(A),l)
| less_than_or_equal(l,A) ),
inference(copy,[status(thm)],[c_4881]) ).
cnf(c_4882,plain,
( less_than_or_equal(l,A)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(g(A),h(l))
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,A) ),
inference(resolve,[status(thm)],[c_39,c_526]) ).
cnf(c_4883,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(g(A),h(l))
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,A) ),
inference(copy,[status(thm)],[c_4882]) ).
cnf(c_4884,plain,
( ~ less_than_or_equal(l,upper_bound)
| less_than_or_equal(g(A),h(l))
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,A) ),
inference(resolve,[status(thm)],[c_50,c_4883]) ).
cnf(c_560,plain,
( less_than_or_equal(g(A),h(l))
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,A) ),
inference(resolve,[status(thm)],[c_43,c_4884]) ).
cnf(c_4885,plain,
( less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(lower_bound,k(l))
| less_than_or_equal(l,h(k(l)))
| less_than_or_equal(f(k(l)),n0)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_164,c_25]) ).
cnf(c_575,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(lower_bound,k(l))
| less_than_or_equal(l,h(k(l)))
| less_than_or_equal(f(k(l)),n0)
| less_than_or_equal(n0,f(l)) ),
inference(copy,[status(thm)],[c_4885]) ).
cnf(c_1888,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(lower_bound,k(l))
| less_than_or_equal(f(k(l)),n0)
| less_than_or_equal(h(k(l)),upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_451,c_6]) ).
cnf(c_4886,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,h(l)) ),
inference(resolve,[status(thm)],[c_560,c_13]) ).
cnf(c_2499,plain,
( less_than_or_equal(f(l),n0)
| less_than_or_equal(l,h(l)) ),
inference(copy,[status(thm)],[c_4886]) ).
cnf(c_4887,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(f(l),n0)
| less_than_or_equal(f(l),n0) ),
inference(resolve,[status(thm)],[c_2499,c_6]) ).
cnf(c_4888,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(f(l),n0) ),
inference(copy,[status(thm)],[c_4887]) ).
cnf(c_4889,plain,
( ~ less_than_or_equal(l,upper_bound)
| less_than_or_equal(f(l),n0) ),
inference(resolve,[status(thm)],[c_50,c_4888]) ).
cnf(c_2508,plain,
less_than_or_equal(f(l),n0),
inference(resolve,[status(thm)],[c_43,c_4889]) ).
cnf(c_2510,plain,
~ less_than_or_equal(n0,f(l)),
inference(resolve,[status(thm)],[c_2508,c_17]) ).
cnf(c_2551,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(lower_bound,k(l))
| less_than_or_equal(f(k(l)),n0)
| less_than_or_equal(h(k(l)),upper_bound) ),
inference(resolve,[status(thm)],[c_2510,c_1888]) ).
cnf(c_2622,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(lower_bound,k(l))
| less_than_or_equal(l,h(k(l)))
| less_than_or_equal(f(k(l)),n0) ),
inference(resolve,[status(thm)],[c_2510,c_575]) ).
cnf(c_2642,plain,
less_than_or_equal(lower_bound,k(l)),
inference(resolve,[status(thm)],[c_2510,c_105]) ).
cnf(c_2644,plain,
less_than_or_equal(k(l),upper_bound),
inference(resolve,[status(thm)],[c_2510,c_71]) ).
cnf(c_4890,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(l,h(k(l)))
| less_than_or_equal(f(k(l)),n0) ),
inference(resolve,[status(thm)],[c_2642,c_2622]) ).
cnf(c_2645,plain,
( less_than_or_equal(l,h(k(l)))
| less_than_or_equal(f(k(l)),n0) ),
inference(resolve,[status(thm)],[c_2644,c_4890]) ).
cnf(c_4891,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(f(k(l)),n0)
| less_than_or_equal(h(k(l)),upper_bound) ),
inference(resolve,[status(thm)],[c_2642,c_2551]) ).
cnf(c_2647,plain,
( less_than_or_equal(f(k(l)),n0)
| less_than_or_equal(h(k(l)),upper_bound) ),
inference(resolve,[status(thm)],[c_2644,c_4891]) ).
cnf(c_4892,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(k(l),l) ),
inference(resolve,[status(thm)],[c_8,c_2510]) ).
cnf(c_4893,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(k(l),l) ),
inference(resolve,[status(thm)],[c_4892,c_50]) ).
cnf(c_2680,plain,
~ less_than_or_equal(k(l),l),
inference(resolve,[status(thm)],[c_4893,c_43]) ).
cnf(c_2686,plain,
~ less_than_or_equal(q(l,k(l)),l),
inference(resolve,[status(thm)],[c_5,c_2680]) ).
cnf(c_2687,plain,
~ less_than_or_equal(k(l),q(l,k(l))),
inference(resolve,[status(thm)],[c_4,c_2680]) ).
cnf(c_4894,plain,
( ~ less_than_or_equal(f(k(l)),n0)
| ~ less_than_or_equal(k(l),upper_bound) ),
inference(resolve,[status(thm)],[c_10,c_2680]) ).
cnf(c_2726,plain,
~ less_than_or_equal(f(k(l)),n0),
inference(resolve,[status(thm)],[c_4894,c_2644]) ).
cnf(c_2736,plain,
less_than_or_equal(h(k(l)),upper_bound),
inference(resolve,[status(thm)],[c_2726,c_2647]) ).
cnf(c_2737,plain,
less_than_or_equal(l,h(k(l))),
inference(resolve,[status(thm)],[c_2726,c_2645]) ).
cnf(c_4895,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(lower_bound,k(l))
| ~ less_than_or_equal(k(l),h(k(l))) ),
inference(resolve,[status(thm)],[c_6,c_2726]) ).
cnf(c_4896,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(k(l),h(k(l))) ),
inference(resolve,[status(thm)],[c_4895,c_2642]) ).
cnf(c_3055,plain,
~ less_than_or_equal(k(l),h(k(l))),
inference(resolve,[status(thm)],[c_4896,c_2644]) ).
cnf(c_3228,plain,
less_than_or_equal(l,q(l,k(l))),
inference(resolve,[status(thm)],[c_2686,c_2]) ).
cnf(c_3229,plain,
~ less_than_or_equal(q(l,k(l)),lower_bound),
inference(resolve,[status(thm)],[c_80,c_2686]) ).
cnf(c_3496,plain,
( less_than_or_equal(n0,f(h(k(l))))
| less_than_or_equal(h(k(l)),l) ),
inference(resolve,[status(thm)],[c_2736,c_33]) ).
cnf(c_4897,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(k(l),h(k(l)))
| ~ less_than_or_equal(n0,f(h(k(l))))
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_2737,c_9]) ).
cnf(c_4898,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(k(l),h(k(l)))
| ~ less_than_or_equal(n0,f(h(k(l)))) ),
inference(resolve,[status(thm)],[c_2510,c_4897]) ).
cnf(c_4899,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(n0,f(h(k(l)))) ),
inference(resolve,[status(thm)],[c_3055,c_4898]) ).
cnf(c_4900,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(n0,f(h(k(l)))) ),
inference(resolve,[status(thm)],[c_50,c_4899]) ).
cnf(c_3560,plain,
~ less_than_or_equal(n0,f(h(k(l)))),
inference(resolve,[status(thm)],[c_43,c_4900]) ).
cnf(c_3564,plain,
less_than_or_equal(h(k(l)),l),
inference(resolve,[status(thm)],[c_3560,c_3496]) ).
cnf(c_4901,plain,
( ~ less_than_or_equal(A,l)
| ~ less_than_or_equal(q(l,k(l)),A) ),
inference(resolve,[status(thm)],[c_3,c_2686]) ).
cnf(c_3703,plain,
~ less_than_or_equal(q(l,k(l)),h(k(l))),
inference(resolve,[status(thm)],[c_4901,c_3564]) ).
cnf(c_4902,plain,
( less_than_or_equal(A,B)
| ~ less_than_or_equal(A,upper_bound)
| less_than_or_equal(B,h(A))
| ~ less_than_or_equal(f(B),n0)
| less_than_or_equal(f(A),n0)
| less_than_or_equal(A,q(l,k(l))) ),
inference(resolve,[status(thm)],[c_182,c_3229]) ).
cnf(c_4903,plain,
( less_than_or_equal(k(l),A)
| ~ less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(A,h(k(l)))
| ~ less_than_or_equal(f(A),n0)
| less_than_or_equal(f(k(l)),n0) ),
inference(resolve,[status(thm)],[c_4902,c_2687]) ).
cnf(c_4904,plain,
( less_than_or_equal(k(l),A)
| ~ less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(A,h(k(l)))
| ~ less_than_or_equal(f(A),n0) ),
inference(resolve,[status(thm)],[c_4903,c_2726]) ).
cnf(c_4905,plain,
( less_than_or_equal(k(l),q(l,k(l)))
| ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(f(q(l,k(l))),n0) ),
inference(resolve,[status(thm)],[c_4904,c_3703]) ).
cnf(c_4906,plain,
( less_than_or_equal(k(l),q(l,k(l)))
| ~ less_than_or_equal(f(q(l,k(l))),n0) ),
inference(resolve,[status(thm)],[c_4905,c_2644]) ).
cnf(c_4782,plain,
~ less_than_or_equal(f(q(l,k(l))),n0),
inference(resolve,[status(thm)],[c_4906,c_2687]) ).
cnf(c_4907,plain,
( less_than_or_equal(f(q(l,k(l))),n0)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(k(l),q(l,k(l)))
| less_than_or_equal(n0,f(l)) ),
inference(resolve,[status(thm)],[c_3228,c_29]) ).
cnf(c_4908,plain,
( less_than_or_equal(f(q(l,k(l))),n0)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| less_than_or_equal(k(l),q(l,k(l))) ),
inference(resolve,[status(thm)],[c_2510,c_4907]) ).
cnf(c_4909,plain,
( less_than_or_equal(f(q(l,k(l))),n0)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l) ),
inference(resolve,[status(thm)],[c_2687,c_4908]) ).
cnf(c_4910,plain,
( less_than_or_equal(f(q(l,k(l))),n0)
| ~ less_than_or_equal(l,upper_bound) ),
inference(resolve,[status(thm)],[c_50,c_4909]) ).
cnf(c_4911,plain,
less_than_or_equal(f(q(l,k(l))),n0),
inference(resolve,[status(thm)],[c_43,c_4910]) ).
cnf(c_4872,plain,
$false,
inference(resolve,[status(thm)],[c_4782,c_4911]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:01:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3641376 was started by sandbox2 on n013,
% 0.09/0.36 % Sat Sep 26 22:01:21 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 84.72/11.26
% 84.72/11.26 % given #500 (A,wt=26): 203 less_than_or_equal(f(A),n0) | less_than_or_equal(A,f(A)) | -less_than_or_equal(f(n0),n0) | less_than_or_equal(n0,h(A)) | -less_than_or_equal(A,upper_bound) | less_than_or_equal(A,lower_bound). [factor(179,a,c)].
% 84.72/11.26
% 84.72/11.26 % SZS status Unsatisfiable for theBenchmark
% 84.72/11.26
% 84.72/11.26 % Proof 1 at 2.15 (+ 0.37) seconds.
% 84.72/11.26 % Length of proof is 62.
% 84.72/11.26 % Level of proof is 14.
% 84.72/11.26 % Maximum clause weight is 28.000.
% 84.72/11.26 % Given clauses 508.
% 84.72/11.26
% 84.72/11.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------