%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 24 unt; 0 def)
% Number of atoms : 79 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 36 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W1,Z,W2] :
( less_equal(W2,Y)
| ~ quotient(X,Z,W2)
| ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f29,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f35,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
! [X,Z] :
( less_equal(X,Z)
| ! [Y] :
( ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f37,plain,
! [X0,X1,X2] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [Y,W2] :
( less_equal(W2,Y)
| ! [X,Z] :
( ~ quotient(X,Z,W2)
| ! [W1] :
( ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
less_equal(x,y),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
quotient(z,y,zQy),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
quotient(z,x,zQx),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
~ less_equal(zQy,zQx),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f67,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f35,f23]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( less_equal(X3,X1)
| ~ quotient(X0,X2,X3)
| ~ less_equal(divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f29,f39]) ).
fof(f105,plain,
! [X0] :
( zQx = X0
| ~ quotient(z,x,X0) ),
inference(resolution,[status(thm)],[f31,f42]) ).
fof(f108,plain,
! [X0,X1] :
( X0 = X1
| ~ quotient(X0,zero,X1) ),
inference(resolution,[status(thm)],[f31,f35]) ).
fof(f109,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f147,plain,
zQx = divide(z,x),
inference(resolution,[status(thm)],[f105,f29]) ).
fof(f178,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f108,f29]) ).
fof(f392,plain,
! [X0,X1,X2] :
( less_equal(X2,X1)
| ~ quotient(X0,divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f83,f67]) ).
fof(f734,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f392,f29]) ).
fof(f753,plain,
! [X0,X1,X2] :
( less_equal(divide(X2,divide(X2,X0)),X1)
| ~ less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f734,f37]) ).
fof(f764,plain,
less_equal(divide(z,zQx),x),
inference(paramodulation,[status(thm)],[f147,f734]) ).
fof(f790,plain,
quotient(divide(z,zQx),x,zero),
inference(resolution,[status(thm)],[f764,f20]) ).
fof(f970,plain,
divide(divide(z,zQx),x) = zero,
inference(resolution,[status(thm)],[f790,f109]) ).
fof(f1544,plain,
! [X0] : less_equal(divide(X0,divide(X0,x)),y),
inference(resolution,[status(thm)],[f753,f40]) ).
fof(f1561,plain,
less_equal(divide(divide(z,zQx),zero),y),
inference(paramodulation,[status(thm)],[f970,f1544]) ).
fof(f1568,plain,
less_equal(divide(z,zQx),y),
inference(forward_demodulation,[status(thm)],[f178,f1561]) ).
fof(f1574,plain,
! [X0] :
( less_equal(X0,zQx)
| ~ quotient(z,y,X0) ),
inference(resolution,[status(thm)],[f1568,f83]) ).
fof(f1620,plain,
less_equal(zQy,zQx),
inference(resolution,[status(thm)],[f1574,f41]) ).
fof(f1622,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1620,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:47:30 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.45 % Refutation found
% 0.13/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.47 % Elapsed time: 0.111829 seconds
% 0.13/0.47 % CPU time: 0.676202 seconds
% 0.13/0.47 % Total memory used: 52.885 MB
% 0.13/0.47 % Net memory used: 51.166 MB
%------------------------------------------------------------------------------