%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:45:22 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.48s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 75 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 38 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
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(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
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(f18,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
! [X,Z] :
( less_equal(X,Z)
| ! [Y] :
( ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f39,plain,
! [X0,X1,X2] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f46,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
idQa != idQ__idQ_idQa,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f55,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f23,f36]) ).
fof(f114,plain,
! [X0,X1] :
( less_equal(X1,idQa)
| ~ quotient(identity,X0,X1)
| ~ less_equal(idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f41,f47]) ).
fof(f115,plain,
! [X0,X1] :
( less_equal(X1,a)
| ~ quotient(identity,X0,X1)
| ~ less_equal(idQa,X0) ),
inference(resolution,[status(thm)],[f41,f46]) ).
fof(f116,plain,
! [X0,X1] :
( less_equal(X1,idQ_idQa)
| ~ quotient(identity,X0,X1)
| ~ less_equal(idQ__idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f41,f48]) ).
fof(f119,plain,
! [X0,X1,X2,X3] :
( less_equal(X3,X1)
| ~ quotient(X0,X2,X3)
| ~ less_equal(divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f41,f31]) ).
fof(f133,plain,
! [X0] :
( less_equal(divide(identity,X0),idQ_idQa)
| ~ less_equal(idQ__idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f116,f31]) ).
fof(f140,plain,
less_equal(divide(identity,idQ__idQ_idQa),idQ_idQa),
inference(resolution,[status(thm)],[f133,f55]) ).
fof(f144,plain,
! [X0] :
( less_equal(divide(identity,idQ__idQ_idQa),X0)
| ~ less_equal(idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f140,f39]) ).
fof(f946,plain,
( less_equal(idQ__idQ_idQa,idQa)
| ~ less_equal(idQ_idQa,idQ_idQa) ),
inference(resolution,[status(thm)],[f114,f48]) ).
fof(f951,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(forward_subsumption_resolution,[status(thm)],[f946,f55]) ).
fof(f952,plain,
( less_equal(idQ_idQa,a)
| ~ less_equal(idQa,idQa) ),
inference(resolution,[status(thm)],[f115,f47]) ).
fof(f959,plain,
less_equal(idQ_idQa,a),
inference(forward_subsumption_resolution,[status(thm)],[f952,f55]) ).
fof(f989,plain,
( idQ__idQ_idQa = idQa
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(resolution,[status(thm)],[f951,f29]) ).
fof(f992,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[f989,f49]) ).
fof(f1070,plain,
less_equal(divide(identity,idQ__idQ_idQa),a),
inference(resolution,[status(thm)],[f959,f144]) ).
fof(f1142,plain,
! [X0] :
( less_equal(X0,idQ__idQ_idQa)
| ~ quotient(identity,a,X0) ),
inference(resolution,[status(thm)],[f1070,f119]) ).
fof(f1488,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(resolution,[status(thm)],[f1142,f46]) ).
fof(f1490,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1488,f992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-2 : 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 : n020.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 20:47:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.48 % Refutation found
% 0.10/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.50 % Elapsed time: 0.117690 seconds
% 0.10/0.50 % CPU time: 0.731548 seconds
% 0.10/0.50 % Total memory used: 52.654 MB
% 0.10/0.50 % Net memory used: 50.796 MB
%------------------------------------------------------------------------------