%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:02:11 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 59 ( 4 unt; 6 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 63 ~; 78 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Z,X,Y] :
( less_or_equal(Z,X)
| ~ less_or_equal(Z,minimum(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Z,X,Y] :
( less_or_equal(Z,Y)
| ~ less_or_equal(Z,minimum(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ~ less_or_equal(minimum(X,Y),n0)
| less_or_equal(Y,n0)
| less_or_equal(X,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Z,Y] :
( less_or_equal(add(X,Y),Z)
| ~ less_or_equal(Y,half(Z))
| ~ less_or_equal(X,half(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( ~ less_or_equal(half(X),n0)
| less_or_equal(X,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [Epsilon] :
( ~ less_or_equal(delta_1(Epsilon),n0)
| less_or_equal(Epsilon,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
! [Epsilon] :
( ~ less_or_equal(delta_2(Epsilon),n0)
| less_or_equal(Epsilon,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [Epsilon,Z] :
( less_or_equal(absolute(add(f(Z),negate(f(a_real_number)))),Epsilon)
| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_1(Epsilon))
| less_or_equal(Epsilon,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [Epsilon,Z] :
( less_or_equal(absolute(add(g(Z),negate(g(a_real_number)))),Epsilon)
| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_2(Epsilon))
| less_or_equal(Epsilon,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [Delta] :
( less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta)
| less_or_equal(Delta,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [Delta] :
( ~ 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)
| less_or_equal(Delta,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [Z,X] :
( less_or_equal(Z,X)
| ! [Y] : ~ less_or_equal(Z,minimum(X,Y)) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [Z,Y] :
( less_or_equal(Z,Y)
| ! [X] : ~ less_or_equal(Z,minimum(X,Y)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X1,n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] :
( less_or_equal(add(X0,X2),X1)
| ~ less_or_equal(X2,half(X1))
| ~ less_or_equal(X0,half(X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1] :
( less_or_equal(absolute(add(f(X1),negate(f(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_1(X0))
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1] :
( less_or_equal(absolute(add(g(X1),negate(g(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_2(X0))
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
~ less_or_equal(epsilon_0,n0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0] :
( ~ 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)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( less_or_equal(minimum(X0,X1),n0)
| less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0) ),
inference(resolution,[status(thm)],[f14,f25]) ).
fof(f44,plain,
! [X0,X1] :
( less_or_equal(minimum(X0,X1),n0)
| less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1) ),
inference(resolution,[status(thm)],[f16,f25]) ).
fof(f45,plain,
! [X0] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(g(xs(X0)),negate(g(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ),
inference(resolution,[status(thm)],[f18,f26]) ).
fof(f60,plain,
! [X0] :
( ~ 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(X0,n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ),
inference(resolution,[status(thm)],[f45,f23]) ).
fof(f61,definition,
! [X0] :
( sQ0_spl
<=> ( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0] :
( ~ sQ0_spl
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ1_spl
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ1_spl
| less_or_equal(half(epsilon_0),n0) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64]) ).
fof(f68,plain,
! [X0] :
( ~ sQ0_spl
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0) ),
inference(resolution,[status(thm)],[f62,f22]) ).
fof(f69,definition,
! [X0] :
( sQ2_spl
<=> ( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f70,plain,
! [X0] :
( ~ sQ2_spl
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( ~ sQ0_spl
| sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f68,f69,f64,f61]) ).
fof(f73,plain,
( ~ sQ1_spl
| less_or_equal(epsilon_0,n0) ),
inference(resolution,[status(thm)],[f65,f19]) ).
fof(f74,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f24]) ).
fof(f75,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f74]) ).
fof(f195,plain,
! [X0] :
( ~ sQ2_spl
| 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) ),
inference(resolution,[status(thm)],[f70,f44]) ).
fof(f215,plain,
! [X0] :
( ~ sQ2_spl
| ~ 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) ),
inference(duplicate_literals_removal,[status(thm)],[f195]) ).
fof(f217,definition,
( sQ3_spl
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ3_spl
| less_or_equal(delta_2(half(epsilon_0)),n0) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f224,plain,
( ~ sQ3_spl
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[status(thm)],[f218,f21]) ).
fof(f225,plain,
( ~ sQ3_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f224,f64,f217]) ).
fof(f349,plain,
( ~ sQ2_spl
| 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) ),
inference(resolution,[status(thm)],[f215,f27]) ).
fof(f361,definition,
( sQ5_spl
<=> less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ5_spl
| less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( ~ sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f349,f361,f69]) ).
fof(f387,plain,
( ~ sQ5_spl
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(resolution,[status(thm)],[f362,f17]) ).
fof(f388,definition,
( sQ6_spl
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( ~ sQ6_spl
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,plain,
( ~ sQ5_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f387,f388,f217,f361]) ).
fof(f392,plain,
( ~ sQ6_spl
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[status(thm)],[f389,f20]) ).
fof(f393,plain,
( ~ sQ6_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f392,f64,f388]) ).
fof(f394,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f72,f75,f225,f364,f391,f393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 : Mon Sep 21 13:19:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.059934 seconds
% 0.09/0.43 % CPU time: 0.223333 seconds
% 0.09/0.43 % Total memory used: 14.680 MB
% 0.09/0.43 % Net memory used: 14.350 MB
%------------------------------------------------------------------------------