%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:45:20 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.57s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 31 unt; 0 def)
% Number of atoms : 79 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 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(f8,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,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(f14,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
less_equal(a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f21,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2)
| ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) ),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f22,plain,
! [X0] : divide(zero,X0) = zero,
inference(resolution,[status(thm)],[f14,f19]) ).
fof(f23,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f14,f15]) ).
fof(f24,plain,
! [X0,X1] :
( divide(divide(X0,X1),divide(zero,X1)) = divide(divide(X0,zero),X1)
| ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero)) ),
inference(paramodulation,[status(thm)],[f22,f21]) ).
fof(f32,plain,
! [X0,X1] :
( divide(divide(X0,X1),zero) = divide(divide(X0,zero),X1)
| ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero)) ),
inference(forward_demodulation,[status(thm)],[f22,f24]) ).
fof(f79,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(resolution,[status(thm)],[f10,f13]) ).
fof(f80,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f81,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[f10,f17]) ).
fof(f169,plain,
! [X0] :
( divide(divide(X0,X0),zero) = divide(divide(X0,zero),X0)
| ~ less_equal(zero,divide(divide(X0,X0),zero)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f182,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),divide(divide(X1,X2),X1)) = divide(divide(X0,divide(X1,X2)),X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(paramodulation,[status(thm)],[f80,f21]) ).
fof(f184,plain,
! [X0,X1,X2] :
( divide(divide(divide(X1,X2),X0),divide(X1,X0)) = divide(divide(divide(X1,X2),X1),X0)
| ~ less_equal(divide(zero,X0),divide(divide(divide(X1,X2),X0),divide(X1,X0))) ),
inference(paramodulation,[status(thm)],[f80,f21]) ).
fof(f190,plain,
! [X0] :
( divide(divide(X0,X0),zero) = zero
| ~ less_equal(zero,divide(divide(X0,X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f80,f169]) ).
fof(f191,plain,
! [X0] : divide(divide(X0,X0),zero) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f190,f14]) ).
fof(f219,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),zero) = divide(divide(X0,divide(X1,X2)),X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(forward_demodulation,[status(thm)],[f80,f182]) ).
fof(f223,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(divide(divide(X0,X1),X0),X2)
| ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f22,f184]) ).
fof(f224,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(zero,X2)
| ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f223]) ).
fof(f225,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero
| ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f22,f224]) ).
fof(f226,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f225,f14]) ).
fof(f242,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f191,f11]) ).
fof(f296,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f242,f23]) ).
fof(f308,plain,
! [X0] :
( divide(divide(X0,divide(X0,zero)),zero) = divide(divide(X0,zero),divide(X0,zero))
| ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero)) ),
inference(paramodulation,[status(thm)],[f296,f32]) ).
fof(f329,plain,
! [X0] :
( divide(divide(X0,divide(X0,zero)),zero) = zero
| ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero)) ),
inference(forward_demodulation,[status(thm)],[f296,f308]) ).
fof(f330,plain,
! [X0] : divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f329,f14]) ).
fof(f382,plain,
! [X0] : divide(divide(divide(X0,b),zero),divide(divide(X0,a),b)) = zero,
inference(paramodulation,[status(thm)],[f81,f79]) ).
fof(f685,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f330,f11]) ).
fof(f750,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f685,f23]) ).
fof(f765,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f750,f11]) ).
fof(f833,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f765,f19]) ).
fof(f928,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),zero) = divide(divide(X0,divide(X1,X2)),X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f833,f219]) ).
fof(f929,plain,
! [X0,X1,X2] :
( divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f833,f928]) ).
fof(f1032,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(X0,X2)),
inference(resolution,[status(thm)],[f226,f11]) ).
fof(f1522,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1),
inference(backward_subsumption_resolution,[status(thm)],[f929,f1032]) ).
fof(f2746,plain,
! [X0] : divide(divide(X0,b),divide(divide(X0,a),b)) = zero,
inference(forward_demodulation,[status(thm)],[f833,f382]) ).
fof(f2785,plain,
! [X0] : divide(divide(X0,b),divide(X0,a)) = divide(zero,divide(X0,a)),
inference(paramodulation,[status(thm)],[f2746,f1522]) ).
fof(f2835,plain,
! [X0] : divide(divide(X0,b),divide(X0,a)) = zero,
inference(forward_demodulation,[status(thm)],[f22,f2785]) ).
fof(f3783,plain,
! [X0] : less_equal(divide(X0,b),divide(X0,a)),
inference(resolution,[status(thm)],[f2835,f11]) ).
fof(f3940,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f18,f3783]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:51:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.15/0.57 % Refutation found
% 0.15/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.59 % Elapsed time: 0.215842 seconds
% 0.15/0.59 % CPU time: 1.396202 seconds
% 0.15/0.59 % Total memory used: 82.445 MB
% 0.15/0.59 % Net memory used: 80.680 MB
%------------------------------------------------------------------------------