%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:45:17 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 20 unt; 0 def)
% Number of atoms : 99 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 54 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 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(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,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,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(f19,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)],[f18]) ).
fof(f20,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0] : quotient(zero,X0,zero),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
~ quotient(x,zero,x),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X2 = divide(X0,X1)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f23,f25]) ).
fof(f80,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[status(thm)],[f67,f14]) ).
fof(f85,plain,
! [X0,X1,X2] :
( zero = divide(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f17,f80]) ).
fof(f108,plain,
! [X0] :
( X0 = zero
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f111,plain,
! [X0,X1] :
( ~ quotient(X1,X0,zero)
| X0 = X1
| ~ less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f21,f15]) ).
fof(f114,plain,
! [X0] :
( ~ quotient(X0,zero,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[f108,f15]) ).
fof(f126,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f85,f23]) ).
fof(f135,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(paramodulation,[status(thm)],[f126,f23]) ).
fof(f169,plain,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| ~ quotient(X1,X0,zero)
| X0 = X1 ),
inference(resolution,[status(thm)],[f111,f15]) ).
fof(f205,plain,
! [X0,X1,X2,X3,X4,X5] :
( less_equal(X4,X5)
| ~ quotient(X1,X2,X5)
| ~ quotient(X3,zero,X4)
| ~ quotient(X0,X2,X3)
| ~ quotient(X0,zero,X1) ),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f304,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(divide(X3,zero),X4)
| ~ quotient(X1,X2,X4)
| ~ quotient(X0,X2,X3)
| ~ quotient(X0,zero,X1) ),
inference(resolution,[status(thm)],[f205,f23]) ).
fof(f314,plain,
! [X0,X1] :
( ~ quotient(X0,divide(X0,X1),zero)
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[f169,f135]) ).
fof(f342,plain,
! [X0,X1,X2,X3] :
( less_equal(divide(X2,zero),X3)
| ~ quotient(divide(X0,zero),X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f304,f23]) ).
fof(f376,plain,
! [X0,X1,X2] :
( less_equal(divide(divide(X0,X1),zero),X2)
| ~ quotient(divide(X0,zero),X1,X2) ),
inference(resolution,[status(thm)],[f342,f23]) ).
fof(f389,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[status(thm)],[f376,f28]) ).
fof(f401,plain,
! [X0] : divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(resolution,[status(thm)],[f389,f108]) ).
fof(f435,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(paramodulation,[status(thm)],[f401,f23]) ).
fof(f455,plain,
! [X0] : divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[f435,f114]) ).
fof(f515,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(paramodulation,[status(thm)],[f455,f23]) ).
fof(f526,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f515,f314]) ).
fof(f582,plain,
! [X0] : quotient(X0,zero,X0),
inference(paramodulation,[status(thm)],[f526,f23]) ).
fof(f586,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f29,f582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:50:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.055606 seconds
% 0.15/0.43 % CPU time: 0.225591 seconds
% 0.15/0.43 % Total memory used: 22.992 MB
% 0.15/0.43 % Net memory used: 22.511 MB
%------------------------------------------------------------------------------