%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 30 unt; 0 def)
% Number of atoms : 74 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : divide(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : divide(X,X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,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(f17,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0] : divide(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0] : divide(X0,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,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)],[f18,f16]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = divide(X0,X1)
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f18,f15]) ).
fof(f28,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[f13,f23]) ).
fof(f30,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f33,plain,
! [X0] :
( X0 = zero
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f17,f18]) ).
fof(f38,plain,
! [X0,X1] :
( divide(divide(X0,X1),divide(X0,X1)) = divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1)))
| ~ less_equal(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f22,f25]) ).
fof(f54,plain,
! [X0,X1] :
( zero = divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1)))
| ~ less_equal(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1)))) ),
inference(forward_demodulation,[status(thm)],[f22,f38]) ).
fof(f55,plain,
! [X0,X1] : zero = divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f54,f17]) ).
fof(f153,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)],[f28,f25]) ).
fof(f164,plain,
( zero = divide(divide(a,d),divide(b,d))
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(forward_demodulation,[status(thm)],[f28,f153]) ).
fof(f165,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(forward_subsumption_resolution,[status(thm)],[f164,f17]) ).
fof(f264,plain,
! [X0,X1,X2] :
( divide(divide(X0,divide(X1,X2)),X1) = divide(divide(X0,X1),divide(divide(X1,X2),X1))
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(paramodulation,[status(thm)],[f30,f25]) ).
fof(f266,plain,
! [X0,X1,X2] :
( divide(divide(divide(X1,X2),X1),X0) = divide(divide(divide(X1,X2),X0),divide(X1,X0))
| ~ less_equal(divide(zero,X0),divide(divide(divide(X1,X2),X0),divide(X1,X0))) ),
inference(paramodulation,[status(thm)],[f30,f25]) ).
fof(f288,plain,
! [X0,X1,X2] :
( divide(divide(X0,divide(X1,X2)),X1) = divide(divide(X0,X1),zero)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(forward_demodulation,[status(thm)],[f30,f264]) ).
fof(f292,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X0),X2) = divide(divide(divide(X0,X1),X2),divide(X0,X2))
| ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f21,f266]) ).
fof(f293,plain,
! [X0,X1,X2] :
( divide(zero,X2) = divide(divide(divide(X0,X1),X2),divide(X0,X2))
| ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f30,f292]) ).
fof(f294,plain,
! [X0,X1,X2] :
( zero = divide(divide(divide(X0,X1),X2),divide(X0,X2))
| ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f21,f293]) ).
fof(f296,plain,
! [X0,X1,X2] : zero = divide(divide(divide(X0,X1),X2),divide(X0,X2)),
inference(forward_subsumption_resolution,[status(thm)],[f294,f17]) ).
fof(f440,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(X0,X2)),
inference(resolution,[status(thm)],[f296,f14]) ).
fof(f631,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(paramodulation,[status(thm)],[f21,f55]) ).
fof(f938,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f631,f14]) ).
fof(f1030,plain,
! [X0] : divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[f938,f33]) ).
fof(f1411,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f1030,f14]) ).
fof(f1523,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f1411,f26]) ).
fof(f1574,plain,
! [X0,X1,X2] :
( divide(divide(X0,divide(X1,X2)),X1) = divide(X0,X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(backward_demodulation,[status(thm)],[f1523,f288]) ).
fof(f1644,plain,
! [X0,X1,X2] :
( divide(divide(X0,divide(X1,X2)),X1) = divide(X0,X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f1523,f1574]) ).
fof(f1646,plain,
! [X0,X1,X2] : divide(divide(X0,divide(X1,X2)),X1) = divide(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f1644,f440]) ).
fof(f2725,plain,
divide(zero,b) = divide(divide(a,d),b),
inference(paramodulation,[status(thm)],[f165,f1646]) ).
fof(f2804,plain,
zero = divide(divide(a,d),b),
inference(forward_demodulation,[status(thm)],[f21,f2725]) ).
fof(f2837,plain,
less_equal(divide(a,d),b),
inference(resolution,[status(thm)],[f2804,f14]) ).
fof(f2882,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2837,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:46:25 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.058233 seconds
% 0.12/0.42 % CPU time: 0.271390 seconds
% 0.12/0.42 % Total memory used: 55.503 MB
% 0.12/0.42 % Net memory used: 55.160 MB
%------------------------------------------------------------------------------