%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:45:19 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 15 unt; 2 def)
% Number of atoms : 62 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
! [X,Z] :
( less_equal(X,Z)
| ! [Y] :
( ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0,X1,X2] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),X2) = divide(divide(X0,X2),divide(X1,X2))
| ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f55,plain,
! [X0] :
( ~ less_equal(X0,b)
| ~ less_equal(divide(a,d),X0) ),
inference(resolution,[status(thm)],[f27,f29]) ).
fof(f127,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[f15,f28]) ).
fof(f162,plain,
! [X0] :
( divide(divide(a,d),X0) != zero
| ~ less_equal(X0,b) ),
inference(resolution,[status(thm)],[f55,f16]) ).
fof(f421,plain,
! [X0] : divide(divide(a,d),divide(b,X0)) != zero,
inference(resolution,[status(thm)],[f162,f17]) ).
fof(f708,plain,
( divide(divide(a,b),d) = divide(divide(a,d),divide(b,d))
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(paramodulation,[status(thm)],[f127,f36]) ).
fof(f725,definition,
( sQ18_spl
<=> less_equal(zero,divide(divide(a,d),divide(b,d))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( sQ18_spl
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f728,definition,
( sQ19_spl
<=> divide(divide(a,b),d) = divide(divide(a,d),divide(b,d)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f729,plain,
( ~ sQ19_spl
| divide(divide(a,b),d) = divide(divide(a,d),divide(b,d)) ),
inference(component_clause,[status(thm)],[f728]) ).
fof(f731,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f708,f725,f728]) ).
fof(f760,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f727,f19]) ).
fof(f761,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f760]) ).
fof(f762,plain,
( ~ sQ19_spl
| zero = divide(divide(a,d),divide(b,d)) ),
inference(forward_demodulation,[status(thm)],[f127,f729]) ).
fof(f763,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f421]) ).
fof(f764,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f763]) ).
fof(f765,plain,
$false,
inference(sat_refutation,[status(thm)],[f731,f761,f764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n005.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 20 20:45:48 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.101041 seconds
% 0.13/0.46 % CPU time: 0.555528 seconds
% 0.13/0.46 % Total memory used: 73.640 MB
% 0.13/0.46 % Net memory used: 72.990 MB
%------------------------------------------------------------------------------