%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:45:18 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 28 unt; 0 def)
% Number of atoms : 97 ( 14 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 94 ( 48 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 101 !; 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(f3,axiom,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
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(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f23,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f32,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
less_equal(x,y),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
less_equal(y,z),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f35,plain,
~ less_equal(x,z),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f23,f24]) ).
fof(f63,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)],[f26,f22]) ).
fof(f64,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f65,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f64,f38]) ).
fof(f71,plain,
quotient(y,z,zero),
inference(resolution,[status(thm)],[f17,f34]) ).
fof(f72,plain,
quotient(x,y,zero),
inference(resolution,[status(thm)],[f17,f33]) ).
fof(f93,plain,
! [X0] :
( zero = X0
| ~ quotient(x,y,X0) ),
inference(resolution,[status(thm)],[f28,f72]) ).
fof(f94,plain,
! [X0] :
( zero = X0
| ~ quotient(y,z,X0) ),
inference(resolution,[status(thm)],[f28,f71]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ~ quotient(X0,zero,X1) ),
inference(resolution,[status(thm)],[f28,f32]) ).
fof(f111,plain,
zero = divide(x,y),
inference(resolution,[status(thm)],[f93,f26]) ).
fof(f116,plain,
zero = divide(y,z),
inference(resolution,[status(thm)],[f94,f26]) ).
fof(f176,plain,
! [X0,X1,X2,X3,X4,X5] :
( less_equal(X4,X5)
| ~ quotient(divide(X0,X3),X1,X5)
| ~ quotient(X2,divide(X3,X1),X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f63,f26]) ).
fof(f187,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f97,f26]) ).
fof(f998,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(divide(X0,X2),X1,X4)
| ~ quotient(divide(X0,X1),divide(X2,X1),X3) ),
inference(resolution,[status(thm)],[f176,f26]) ).
fof(f1043,plain,
! [X0,X1,X2,X3] :
( less_equal(divide(divide(X0,X2),divide(X1,X2)),X3)
| ~ quotient(divide(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f998,f26]) ).
fof(f1077,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(resolution,[status(thm)],[f1043,f26]) ).
fof(f1132,plain,
! [X0] : less_equal(divide(divide(X0,z),zero),divide(divide(X0,y),z)),
inference(paramodulation,[status(thm)],[f116,f1077]) ).
fof(f1174,plain,
! [X0] : less_equal(divide(X0,z),divide(divide(X0,y),z)),
inference(forward_demodulation,[status(thm)],[f187,f1132]) ).
fof(f1572,plain,
less_equal(divide(x,z),divide(zero,z)),
inference(paramodulation,[status(thm)],[f111,f1174]) ).
fof(f1585,plain,
less_equal(divide(x,z),zero),
inference(forward_demodulation,[status(thm)],[f65,f1572]) ).
fof(f1590,plain,
zero = divide(x,z),
inference(resolution,[status(thm)],[f1585,f38]) ).
fof(f1631,plain,
quotient(x,z,zero),
inference(paramodulation,[status(thm)],[f1590,f26]) ).
fof(f1651,plain,
less_equal(x,z),
inference(resolution,[status(thm)],[f1631,f18]) ).
fof(f1669,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1651,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:48:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % 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
% 0.13/0.45 % Elapsed time: 0.091984 seconds
% 0.13/0.45 % CPU time: 0.505082 seconds
% 0.13/0.45 % Total memory used: 49.171 MB
% 0.13/0.45 % Net memory used: 47.899 MB
%------------------------------------------------------------------------------