%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN010-2 : 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 12:45:23 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.60s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 106 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 59 ~; 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 : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y1,Y2,Y3] :
( Y1 = Y3
| ~ quotient(identity,Y2,Y3)
| ~ quotient(identity,Y1,Y2)
| ~ quotient(identity,X,Y1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f29,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
! [Y1,Y3] :
( Y1 = Y3
| ! [Y2] :
( ~ quotient(identity,Y2,Y3)
| ~ quotient(identity,Y1,Y2)
| ! [X] : ~ quotient(identity,X,Y1) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(resolution,[status(thm)],[f26,f51]) ).
fof(f68,plain,
( idQa_Q__idQ_idQa = idQa
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(resolution,[status(thm)],[f30,f55]) ).
fof(f69,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f30,f29]) ).
fof(f72,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[f68,f52]) ).
fof(f78,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f138,plain,
! [X0,X1] :
( idQa = X1
| ~ quotient(identity,X0,X1)
| ~ quotient(identity,idQa,X0) ),
inference(resolution,[status(thm)],[f49,f48]) ).
fof(f179,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(idQ_idQa,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient(idQa,X0,X1) ),
inference(resolution,[status(thm)],[f50,f28]) ).
fof(f224,plain,
! [X0] : divide(X0,X0) = zero,
inference(resolution,[status(thm)],[f78,f37]) ).
fof(f512,plain,
! [X0] :
( idQa = X0
| ~ quotient(identity,idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f138,f50]) ).
fof(f578,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(idQ_idQa,idQ_idQa,X2)
| ~ quotient(X0,idQa_Q__idQ_idQa,X1)
| ~ quotient(identity,idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f179,f51]) ).
fof(f617,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(idQ_idQa,idQ_idQa,X1)
| ~ quotient(divide(identity,idQ_idQa),idQa_Q__idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f578,f32]) ).
fof(f621,plain,
! [X0] :
( less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),X0)
| ~ quotient(idQ_idQa,idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f617,f32]) ).
fof(f831,plain,
idQa = divide(identity,idQ_idQa),
inference(resolution,[status(thm)],[f512,f32]) ).
fof(f1274,plain,
! [X0] :
( less_equal(divide(idQa,idQa_Q__idQ_idQa),X0)
| ~ quotient(idQ_idQa,idQ_idQa,X0) ),
inference(forward_demodulation,[status(thm)],[f831,f621]) ).
fof(f1275,plain,
less_equal(divide(idQa,idQa_Q__idQ_idQa),divide(idQ_idQa,idQ_idQa)),
inference(resolution,[status(thm)],[f1274,f32]) ).
fof(f1277,plain,
less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(forward_demodulation,[status(thm)],[f224,f1275]) ).
fof(f1279,plain,
zero = divide(idQa,idQa_Q__idQ_idQa),
inference(resolution,[status(thm)],[f1277,f69]) ).
fof(f1310,plain,
quotient(idQa,idQa_Q__idQ_idQa,zero),
inference(paramodulation,[status(thm)],[f1279,f32]) ).
fof(f1343,plain,
less_equal(idQa,idQa_Q__idQ_idQa),
inference(resolution,[status(thm)],[f1310,f24]) ).
fof(f1364,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1343,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n002.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sun Sep 20 20:49:13 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Drodi V4.1.1
% 0.13/10.60 % Refutation found
% 0.13/10.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.60 % Elapsed time: 0.219297 seconds
% 0.13/10.60 % CPU time: 1.520296 seconds
% 0.13/10.60 % Total memory used: 60.694 MB
% 0.13/10.60 % Net memory used: 56.839 MB
%------------------------------------------------------------------------------