%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:45:21 PM UTC 2026
% Result : Unsatisfiable 2.76s 0.80s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 28 unt; 0 def)
% Number of atoms : 109 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 58 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 108 ( 108 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
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(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : quotient(zero,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [V4,V5] :
( less_equal(V4,V5)
| ! [V1,Z] :
( ~ quotient(V1,Z,V5)
| ! [V2,V3] :
( ~ quotient(V3,V2,V4)
| ! [X] :
( ~ quotient(X,Z,V3)
| ! [Y] :
( ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] : quotient(zero,X0,zero),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,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(f40,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)],[f39]) ).
fof(f43,plain,
less_equal(a,b),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f44,plain,
quotient(a,c,aQc),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f45,plain,
quotient(b,c,bQc),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f46,plain,
~ less_equal(aQc,bQc),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f27,f28]) ).
fof(f65,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f22,f35]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( less_equal(X3,X1)
| ~ quotient(X0,X2,X3)
| ~ less_equal(divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f30,f40]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( less_equal(X5,X6)
| ~ quotient(divide(X3,X0),X1,X6)
| ~ quotient(X4,X2,X5)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f70,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f30]) ).
fof(f125,plain,
! [X0,X1] :
( X0 = X1
| ~ quotient(X0,zero,X1) ),
inference(resolution,[status(thm)],[f36,f32]) ).
fof(f129,plain,
quotient(a,b,zero),
inference(resolution,[status(thm)],[f43,f21]) ).
fof(f144,plain,
! [X0,X1,X2] :
( less_equal(X2,X1)
| ~ quotient(X0,divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f66,f65]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,b),c,X3)
| ~ quotient(X1,bQc,X2)
| ~ quotient(X0,c,X1) ),
inference(resolution,[status(thm)],[f67,f45]) ).
fof(f214,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f125,f30]) ).
fof(f291,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[f129,f70]) ).
fof(f568,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f144,f30]) ).
fof(f583,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(divide(a,b),c,X1)
| ~ quotient(aQc,bQc,X0) ),
inference(resolution,[status(thm)],[f145,f44]) ).
fof(f588,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(zero,c,X1)
| ~ quotient(aQc,bQc,X0) ),
inference(forward_demodulation,[status(thm)],[f291,f583]) ).
fof(f1324,plain,
! [X0] :
( less_equal(divide(aQc,bQc),X0)
| ~ quotient(zero,c,X0) ),
inference(resolution,[status(thm)],[f588,f30]) ).
fof(f3763,plain,
less_equal(divide(aQc,bQc),zero),
inference(resolution,[status(thm)],[f1324,f34]) ).
fof(f3767,plain,
zero = divide(aQc,bQc),
inference(resolution,[status(thm)],[f3763,f55]) ).
fof(f3816,plain,
less_equal(divide(aQc,zero),bQc),
inference(paramodulation,[status(thm)],[f3767,f568]) ).
fof(f3847,plain,
less_equal(aQc,bQc),
inference(forward_demodulation,[status(thm)],[f214,f3816]) ).
fof(f3848,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3847,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:46:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 2.76/0.80 % Refutation found
% 2.76/0.80 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.76/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.83 % Elapsed time: 0.443523 seconds
% 0.27/0.83 % CPU time: 3.263129 seconds
% 0.27/0.83 % Total memory used: 75.823 MB
% 0.27/0.83 % Net memory used: 68.260 MB
%------------------------------------------------------------------------------