%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 1.03s 0.59s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 121 ( 65 unt; 0 def)
% Number of atoms : 232 ( 33 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 225 ( 114 ~; 111 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 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 : 200 ( 200 !; 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(f7,axiom,
! [X] : less_equal(X,identity),
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(f10,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
idQa != idQ__idQ_idQa,
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(f22,plain,
! [X0] : less_equal(X0,identity),
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f26,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
idQa != idQ__idQ_idQa,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0] : quotient(zero,X0,zero),
inference(resolution,[status(thm)],[f14,f20]) ).
fof(f31,plain,
! [X0] : quotient(X0,identity,zero),
inference(resolution,[status(thm)],[f14,f22]) ).
fof(f37,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f38,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f37,f14]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(idQa,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient(a,X0,X1) ),
inference(resolution,[status(thm)],[f19,f26]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(idQ__idQ_idQa,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient(idQ_idQa,X0,X1) ),
inference(resolution,[status(thm)],[f19,f28]) ).
fof(f49,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)],[f19,f23]) ).
fof(f50,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f21,f37]) ).
fof(f51,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f61,plain,
! [X0] :
( idQ_idQa = X0
| ~ quotient(identity,idQa,X0) ),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f64,plain,
! [X0,X1] :
( zero = X1
| ~ quotient(X0,identity,X1) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f65,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f72,plain,
! [X0] : zero = divide(X0,identity),
inference(resolution,[status(thm)],[f64,f23]) ).
fof(f79,plain,
idQ_idQa = divide(identity,idQa),
inference(resolution,[status(thm)],[f61,f23]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(idQa,X0,X3)
| ~ quotient(X1,divide(a,X0),X2)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[f46,f23]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(idQ__idQ_idQa,X0,X3)
| ~ quotient(X1,divide(idQ_idQa,X0),X2)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f107,plain,
! [X0,X1,X2] :
( less_equal(divide(X1,divide(idQ_idQa,X0)),X2)
| ~ quotient(idQ__idQ_idQa,X0,X2)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[f93,f23]) ).
fof(f110,plain,
! [X0] :
( less_equal(divide(idQa,divide(idQ_idQa,a)),X0)
| ~ quotient(idQ__idQ_idQa,a,X0) ),
inference(resolution,[status(thm)],[f107,f26]) ).
fof(f118,plain,
less_equal(divide(idQa,divide(idQ_idQa,a)),divide(idQ__idQ_idQa,a)),
inference(resolution,[status(thm)],[f110,f23]) ).
fof(f120,plain,
quotient(divide(idQa,divide(idQ_idQa,a)),divide(idQ__idQ_idQa,a),zero),
inference(resolution,[status(thm)],[f118,f14]) ).
fof(f143,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f65,f38]) ).
fof(f258,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(divide(X0,zero),X1,X4)
| ~ quotient(X2,zero,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f49,f30]) ).
fof(f259,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,identity),idQa,X3)
| ~ quotient(X1,idQ_idQa,X2)
| ~ quotient(X0,idQa,X1) ),
inference(resolution,[status(thm)],[f49,f27]) ).
fof(f260,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,identity),a,X3)
| ~ quotient(X1,idQa,X2)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[f49,f26]) ).
fof(f261,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,identity),idQ_idQa,X3)
| ~ quotient(X1,idQ__idQ_idQa,X2)
| ~ quotient(X0,idQ_idQa,X1) ),
inference(resolution,[status(thm)],[f49,f28]) ).
fof(f263,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)],[f49,f23]) ).
fof(f264,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(zero,idQa,X3)
| ~ quotient(X1,idQ_idQa,X2)
| ~ quotient(X0,idQa,X1) ),
inference(forward_demodulation,[status(thm)],[f72,f259]) ).
fof(f265,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(zero,a,X3)
| ~ quotient(X1,idQa,X2)
| ~ quotient(X0,a,X1) ),
inference(forward_demodulation,[status(thm)],[f72,f260]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(zero,idQ_idQa,X3)
| ~ quotient(X1,idQ__idQ_idQa,X2)
| ~ quotient(X0,idQ_idQa,X1) ),
inference(forward_demodulation,[status(thm)],[f72,f261]) ).
fof(f307,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(zero,idQ_idQa,X2)
| ~ quotient(divide(X0,idQ_idQa),idQ__idQ_idQa,X1) ),
inference(resolution,[status(thm)],[f266,f23]) ).
fof(f393,plain,
! [X0,X1] :
( less_equal(divide(divide(X1,idQ_idQa),idQ__idQ_idQa),X0)
| ~ quotient(zero,idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f307,f23]) ).
fof(f397,plain,
! [X0] : less_equal(divide(divide(X0,idQ_idQa),idQ__idQ_idQa),zero),
inference(resolution,[status(thm)],[f393,f30]) ).
fof(f400,plain,
! [X0] : zero = divide(divide(X0,idQ_idQa),idQ__idQ_idQa),
inference(resolution,[status(thm)],[f397,f51]) ).
fof(f423,plain,
! [X0] : quotient(divide(X0,idQ_idQa),idQ__idQ_idQa,zero),
inference(paramodulation,[status(thm)],[f400,f23]) ).
fof(f427,plain,
! [X0] : less_equal(divide(X0,idQ_idQa),idQ__idQ_idQa),
inference(resolution,[status(thm)],[f423,f15]) ).
fof(f437,plain,
! [X0] :
( divide(X0,idQ_idQa) = idQ__idQ_idQa
| ~ less_equal(idQ__idQ_idQa,divide(X0,idQ_idQa)) ),
inference(resolution,[status(thm)],[f427,f21]) ).
fof(f471,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(zero,idQa,X1)
| ~ quotient(idQ_idQa,idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f264,f27]) ).
fof(f472,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(zero,idQa,X2)
| ~ quotient(divide(X0,idQa),idQ_idQa,X1) ),
inference(resolution,[status(thm)],[f264,f23]) ).
fof(f478,plain,
! [X0,X1,X2] :
( less_equal(divide(X1,divide(a,X0)),X2)
| ~ quotient(idQa,X0,X2)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[f91,f23]) ).
fof(f493,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,zero),X1,X3)
| ~ quotient(divide(X0,X1),zero,X2) ),
inference(resolution,[status(thm)],[f258,f23]) ).
fof(f497,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(zero,a,X1)
| ~ quotient(idQa,idQa,X0) ),
inference(resolution,[status(thm)],[f265,f26]) ).
fof(f498,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(zero,a,X2)
| ~ quotient(divide(X0,a),idQa,X1) ),
inference(resolution,[status(thm)],[f265,f23]) ).
fof(f574,plain,
! [X0] :
( less_equal(divide(idQ_idQa,idQ_idQa),X0)
| ~ quotient(zero,idQa,X0) ),
inference(resolution,[status(thm)],[f471,f23]) ).
fof(f575,plain,
less_equal(divide(idQ_idQa,idQ_idQa),zero),
inference(resolution,[status(thm)],[f574,f30]) ).
fof(f578,plain,
zero = divide(idQ_idQa,idQ_idQa),
inference(resolution,[status(thm)],[f575,f51]) ).
fof(f655,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(divide(identity,X0),idQ_idQa,X2)
| ~ quotient(idQ__idQ_idQa,divide(X0,idQ_idQa),X1) ),
inference(resolution,[status(thm)],[f263,f28]) ).
fof(f694,plain,
! [X0,X1] :
( less_equal(divide(idQ__idQ_idQa,divide(X0,idQ_idQa)),X1)
| ~ quotient(divide(identity,X0),idQ_idQa,X1) ),
inference(resolution,[status(thm)],[f655,f23]) ).
fof(f704,plain,
! [X0] : less_equal(divide(idQ__idQ_idQa,divide(X0,idQ_idQa)),divide(divide(identity,X0),idQ_idQa)),
inference(resolution,[status(thm)],[f694,f23]) ).
fof(f716,plain,
! [X0] :
( less_equal(divide(idQa,idQa),X0)
| ~ quotient(zero,a,X0) ),
inference(resolution,[status(thm)],[f497,f23]) ).
fof(f717,plain,
less_equal(divide(idQa,idQa),zero),
inference(resolution,[status(thm)],[f716,f30]) ).
fof(f720,plain,
zero = divide(idQa,idQa),
inference(resolution,[status(thm)],[f717,f51]) ).
fof(f732,plain,
quotient(idQa,idQa,zero),
inference(paramodulation,[status(thm)],[f720,f23]) ).
fof(f779,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),divide(idQ_idQa,idQ_idQa)),
inference(paramodulation,[status(thm)],[f79,f704]) ).
fof(f786,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(forward_demodulation,[status(thm)],[f578,f779]) ).
fof(f790,plain,
zero = divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolution,[status(thm)],[f786,f51]) ).
fof(f806,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(paramodulation,[status(thm)],[f790,f23]) ).
fof(f816,plain,
less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolution,[status(thm)],[f806,f15]) ).
fof(f828,plain,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(resolution,[status(thm)],[f816,f437]) ).
fof(f844,plain,
( divide(idQa,idQ_idQa) = idQa
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(paramodulation,[status(thm)],[f828,f50]) ).
fof(f854,plain,
( idQ__idQ_idQa = idQa
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(forward_demodulation,[status(thm)],[f828,f844]) ).
fof(f855,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[f854,f29]) ).
fof(f1127,plain,
! [X0,X1] :
( less_equal(divide(divide(X1,idQa),idQ_idQa),X0)
| ~ quotient(zero,idQa,X0) ),
inference(resolution,[status(thm)],[f472,f23]) ).
fof(f1134,plain,
! [X0] : less_equal(divide(divide(X0,idQa),idQ_idQa),zero),
inference(resolution,[status(thm)],[f1127,f30]) ).
fof(f1303,plain,
! [X0] : zero = divide(divide(X0,idQa),idQ_idQa),
inference(resolution,[status(thm)],[f1134,f51]) ).
fof(f1350,plain,
! [X0] : quotient(divide(X0,idQa),idQ_idQa,zero),
inference(paramodulation,[status(thm)],[f1303,f23]) ).
fof(f1366,plain,
! [X0] : less_equal(divide(X0,idQa),idQ_idQa),
inference(resolution,[status(thm)],[f1350,f15]) ).
fof(f1387,plain,
! [X0] :
( divide(X0,idQa) = idQ_idQa
| ~ less_equal(idQ_idQa,divide(X0,idQa)) ),
inference(resolution,[status(thm)],[f1366,f21]) ).
fof(f1447,plain,
! [X0] :
( less_equal(divide(idQ_idQa,divide(a,idQa)),X0)
| ~ quotient(idQa,idQa,X0) ),
inference(resolution,[status(thm)],[f478,f27]) ).
fof(f1565,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(resolution,[status(thm)],[f1447,f732]) ).
fof(f1568,plain,
zero = divide(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[f1565,f51]) ).
fof(f1589,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(paramodulation,[status(thm)],[f1568,f23]) ).
fof(f1595,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[f1589,f15]) ).
fof(f1607,plain,
divide(a,idQa) = idQ_idQa,
inference(resolution,[status(thm)],[f1595,f1387]) ).
fof(f1626,plain,
divide(idQ_idQa,a) = zero,
inference(paramodulation,[status(thm)],[f1607,f143]) ).
fof(f1823,plain,
quotient(divide(idQa,zero),divide(idQ__idQ_idQa,a),zero),
inference(backward_demodulation,[status(thm)],[f1626,f120]) ).
fof(f1890,plain,
! [X0,X1,X2] :
( less_equal(divide(divide(X0,X1),zero),X2)
| ~ quotient(divide(X0,zero),X1,X2) ),
inference(resolution,[status(thm)],[f493,f23]) ).
fof(f1919,plain,
! [X0,X1] :
( less_equal(divide(divide(X1,a),idQa),X0)
| ~ quotient(zero,a,X0) ),
inference(resolution,[status(thm)],[f498,f23]) ).
fof(f2171,plain,
! [X0] : less_equal(divide(divide(X0,a),idQa),zero),
inference(resolution,[status(thm)],[f1919,f30]) ).
fof(f2174,plain,
! [X0] : zero = divide(divide(X0,a),idQa),
inference(resolution,[status(thm)],[f2171,f51]) ).
fof(f2217,plain,
! [X0] : quotient(divide(X0,a),idQa,zero),
inference(paramodulation,[status(thm)],[f2174,f23]) ).
fof(f2224,plain,
! [X0] : less_equal(divide(X0,a),idQa),
inference(resolution,[status(thm)],[f2217,f15]) ).
fof(f2244,plain,
! [X0] :
( divide(X0,a) = idQa
| ~ less_equal(idQa,divide(X0,a)) ),
inference(resolution,[status(thm)],[f2224,f21]) ).
fof(f2542,plain,
less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero),
inference(resolution,[status(thm)],[f1890,f1823]) ).
fof(f2672,plain,
zero = divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(resolution,[status(thm)],[f2542,f51]) ).
fof(f2692,plain,
quotient(divide(idQa,divide(idQ__idQ_idQa,a)),zero,zero),
inference(paramodulation,[status(thm)],[f2672,f23]) ).
fof(f2700,plain,
less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(resolution,[status(thm)],[f2692,f15]) ).
fof(f2719,plain,
zero = divide(idQa,divide(idQ__idQ_idQa,a)),
inference(resolution,[status(thm)],[f2700,f51]) ).
fof(f2742,plain,
quotient(idQa,divide(idQ__idQ_idQa,a),zero),
inference(paramodulation,[status(thm)],[f2719,f23]) ).
fof(f2750,plain,
less_equal(idQa,divide(idQ__idQ_idQa,a)),
inference(resolution,[status(thm)],[f2742,f15]) ).
fof(f2764,plain,
divide(idQ__idQ_idQa,a) = idQa,
inference(resolution,[status(thm)],[f2750,f2244]) ).
fof(f2804,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(paramodulation,[status(thm)],[f2764,f37]) ).
fof(f2826,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2804,f855]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:51:23 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 1.03/0.59 % Refutation found
% 1.03/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.03/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.03/0.60 % Elapsed time: 0.237045 seconds
% 1.03/0.60 % CPU time: 1.593330 seconds
% 1.03/0.60 % Total memory used: 63.484 MB
% 1.03/0.60 % Net memory used: 60.084 MB
%------------------------------------------------------------------------------