%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 0.16s 0.62s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 62 ( 4 unt; 6 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 155 ( 67 ~; 82 |; 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 : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] :
( less_or_equal(absolute(add(X,Y)),Z)
| ~ less_or_equal(add(absolute(X),absolute(Y)),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Z,X,Y] :
( less_or_equal(Z,X)
| ~ less_or_equal(Z,minimum(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Z,X,Y] :
( less_or_equal(Z,Y)
| ~ less_or_equal(Z,minimum(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ~ less_or_equal(minimum(X,Y),n0)
| less_or_equal(Y,n0)
| less_or_equal(X,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( ~ less_or_equal(half(X),n0)
| less_or_equal(X,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
! [Epsilon] :
( ~ less_or_equal(delta_1(Epsilon),n0)
| less_or_equal(Epsilon,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [Epsilon] :
( ~ less_or_equal(delta_2(Epsilon),n0)
| less_or_equal(Epsilon,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [Delta] :
( less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta)
| less_or_equal(Delta,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [Delta] :
( ~ 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)
| less_or_equal(Delta,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1,X2] :
( less_or_equal(absolute(add(X0,X1)),X2)
| ~ less_or_equal(add(absolute(X0),absolute(X1)),X2) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [Z,X] :
( less_or_equal(Z,X)
| ! [Y] : ~ less_or_equal(Z,minimum(X,Y)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [Z,Y] :
( less_or_equal(Z,Y)
| ! [X] : ~ less_or_equal(Z,minimum(X,Y)) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,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)],[f4]) ).
fof(f20,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)],[f5]) ).
fof(f21,plain,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,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)],[f9]) ).
fof(f25,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)],[f10]) ).
fof(f26,plain,
~ less_or_equal(epsilon_0,n0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] :
( ~ 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)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,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)],[f16,f27]) ).
fof(f62,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)],[f18,f27]) ).
fof(f63,plain,
! [X0,X1,X2] :
( less_or_equal(absolute(add(X0,X2)),X1)
| ~ less_or_equal(absolute(X2),half(X1))
| ~ less_or_equal(absolute(X0),half(X1)) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f68,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)],[f63,f28]) ).
fof(f257,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)],[f68,f25]) ).
fof(f259,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(f260,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)],[f259]) ).
fof(f262,definition,
( sQ1_spl
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( ~ sQ1_spl
| less_or_equal(half(epsilon_0),n0) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f257,f259,f262]) ).
fof(f286,plain,
( ~ sQ1_spl
| less_or_equal(epsilon_0,n0) ),
inference(resolution,[status(thm)],[f263,f21]) ).
fof(f287,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f26]) ).
fof(f288,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f333,definition,
( sQ7_spl
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ7_spl
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f347,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)],[f260,f24]) ).
fof(f349,definition,
! [X0] :
( sQ11_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,[sQ11_spl])],[split_symbol_definition]) ).
fof(f350,plain,
! [X0] :
( ~ sQ11_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)],[f349]) ).
fof(f352,plain,
( ~ sQ0_spl
| sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f347,f349,f262,f259]) ).
fof(f357,plain,
( ~ sQ7_spl
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[status(thm)],[f334,f22]) ).
fof(f358,plain,
( ~ sQ7_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f357,f262,f333]) ).
fof(f651,plain,
! [X0] :
( ~ sQ11_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)],[f350,f62]) ).
fof(f680,plain,
! [X0] :
( ~ sQ11_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)],[f651]) ).
fof(f682,definition,
( sQ19_spl
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f683,plain,
( ~ sQ19_spl
| less_or_equal(delta_2(half(epsilon_0)),n0) ),
inference(component_clause,[status(thm)],[f682]) ).
fof(f693,plain,
( ~ sQ19_spl
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[status(thm)],[f683,f23]) ).
fof(f694,plain,
( ~ sQ19_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f693,f262,f682]) ).
fof(f746,plain,
( ~ sQ11_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)],[f680,f29]) ).
fof(f767,definition,
( sQ23_spl
<=> less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f768,plain,
( ~ sQ23_spl
| less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0) ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f770,plain,
( ~ sQ11_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f746,f767,f349]) ).
fof(f775,plain,
( ~ sQ23_spl
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(resolution,[status(thm)],[f768,f19]) ).
fof(f776,plain,
( ~ sQ23_spl
| sQ19_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f775,f333,f682,f767]) ).
fof(f777,plain,
$false,
inference(sat_refutation,[status(thm)],[f265,f288,f352,f358,f694,f770,f776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n019.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 13:22:19 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.62 % Refutation found
% 0.16/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.66 % Elapsed time: 0.211013 seconds
% 0.16/0.66 % CPU time: 1.339461 seconds
% 0.16/0.66 % Total memory used: 44.013 MB
% 0.16/0.66 % Net memory used: 42.324 MB
%------------------------------------------------------------------------------