%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 1.34s 0.67s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 109 ( 62 unt; 0 def)
% Number of atoms : 202 ( 29 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 189 ( 96 ~; 93 |; 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 : 183 ( 183 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : less_equal(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox2/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(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
idQa != idQa_Q__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)],[f22,f14]) ).
fof(f36,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f37,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f36,f14]) ).
fof(f39,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(f42,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(f45,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(idQa_Q__idQ_idQa,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ quotient(idQa,X0,X2)
| ~ quotient(idQ_idQa,X0,X1) ),
inference(resolution,[status(thm)],[f28,f19]) ).
fof(f46,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(resolution,[status(thm)],[f28,f17]) ).
fof(f47,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f21,f36]) ).
fof(f48,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f50,plain,
( idQa_Q__idQ_idQa = idQa
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(resolution,[status(thm)],[f46,f21]) ).
fof(f52,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[f50,f29]) ).
fof(f57,plain,
! [X0,X1] :
( zero = X1
| ~ quotient(X0,identity,X1) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f58,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f64,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)],[f39,f23]) ).
fof(f72,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)],[f42,f27]) ).
fof(f73,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)],[f42,f26]) ).
fof(f74,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)],[f42,f30]) ).
fof(f92,plain,
! [X0] : zero = divide(X0,identity),
inference(resolution,[status(thm)],[f57,f23]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(idQa_Q__idQ_idQa,X0,X3)
| ~ quotient(X1,divide(idQ_idQa,X0),X2)
| ~ quotient(idQa,X0,X1) ),
inference(resolution,[status(thm)],[f45,f23]) ).
fof(f112,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f58,f37]) ).
fof(f188,plain,
! [X0,X1,X2] :
( less_equal(divide(X1,divide(a,X0)),X2)
| ~ quotient(idQa,X0,X2)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[f64,f23]) ).
fof(f201,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)],[f92,f72]) ).
fof(f206,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(zero,idQa,X2)
| ~ quotient(divide(X0,idQa),idQ_idQa,X1) ),
inference(resolution,[status(thm)],[f201,f23]) ).
fof(f210,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)],[f92,f73]) ).
fof(f212,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(zero,a,X1)
| ~ quotient(idQa,idQa,X0) ),
inference(resolution,[status(thm)],[f210,f26]) ).
fof(f214,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(zero,a,X2)
| ~ quotient(divide(X0,a),idQa,X1) ),
inference(resolution,[status(thm)],[f210,f23]) ).
fof(f226,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)],[f74,f23]) ).
fof(f287,plain,
! [X0] :
( less_equal(divide(idQa,idQa),X0)
| ~ quotient(zero,a,X0) ),
inference(resolution,[status(thm)],[f212,f23]) ).
fof(f288,plain,
less_equal(divide(idQa,idQa),zero),
inference(resolution,[status(thm)],[f287,f30]) ).
fof(f294,plain,
zero = divide(idQa,idQa),
inference(resolution,[status(thm)],[f288,f48]) ).
fof(f306,plain,
quotient(idQa,idQa,zero),
inference(paramodulation,[status(thm)],[f294,f23]) ).
fof(f310,plain,
! [X0,X1,X2] :
( less_equal(divide(X1,divide(idQ_idQa,X0)),X2)
| ~ quotient(idQa_Q__idQ_idQa,X0,X2)
| ~ quotient(idQa,X0,X1) ),
inference(resolution,[status(thm)],[f99,f23]) ).
fof(f389,plain,
! [X0,X1] :
( less_equal(divide(divide(X1,idQa),idQ_idQa),X0)
| ~ quotient(zero,idQa,X0) ),
inference(resolution,[status(thm)],[f206,f23]) ).
fof(f395,plain,
! [X0] : less_equal(divide(divide(X0,idQa),idQ_idQa),zero),
inference(resolution,[status(thm)],[f389,f30]) ).
fof(f398,plain,
! [X0] : zero = divide(divide(X0,idQa),idQ_idQa),
inference(resolution,[status(thm)],[f395,f48]) ).
fof(f428,plain,
! [X0] : quotient(divide(X0,idQa),idQ_idQa,zero),
inference(paramodulation,[status(thm)],[f398,f23]) ).
fof(f446,plain,
! [X0] : less_equal(divide(X0,idQa),idQ_idQa),
inference(resolution,[status(thm)],[f428,f15]) ).
fof(f462,plain,
! [X0] :
( divide(X0,idQa) = idQ_idQa
| ~ less_equal(idQ_idQa,divide(X0,idQa)) ),
inference(resolution,[status(thm)],[f446,f21]) ).
fof(f494,plain,
! [X0,X1] :
( less_equal(divide(divide(X1,a),idQa),X0)
| ~ quotient(zero,a,X0) ),
inference(resolution,[status(thm)],[f214,f23]) ).
fof(f498,plain,
! [X0] : less_equal(divide(divide(X0,a),idQa),zero),
inference(resolution,[status(thm)],[f494,f30]) ).
fof(f517,plain,
! [X0] : zero = divide(divide(X0,a),idQa),
inference(resolution,[status(thm)],[f498,f48]) ).
fof(f548,plain,
! [X0] : quotient(divide(X0,a),idQa,zero),
inference(paramodulation,[status(thm)],[f517,f23]) ).
fof(f551,plain,
! [X0] :
( less_equal(divide(idQ_idQa,divide(a,idQa)),X0)
| ~ quotient(idQa,idQa,X0) ),
inference(resolution,[status(thm)],[f188,f27]) ).
fof(f552,plain,
! [X0] :
( less_equal(divide(idQa,divide(a,a)),X0)
| ~ quotient(idQa,a,X0) ),
inference(resolution,[status(thm)],[f188,f26]) ).
fof(f560,plain,
! [X0] : less_equal(divide(X0,a),idQa),
inference(resolution,[status(thm)],[f548,f15]) ).
fof(f579,plain,
! [X0] :
( divide(X0,a) = idQa
| ~ less_equal(idQa,divide(X0,a)) ),
inference(resolution,[status(thm)],[f560,f21]) ).
fof(f655,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(resolution,[status(thm)],[f551,f306]) ).
fof(f658,plain,
zero = divide(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[f655,f48]) ).
fof(f672,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(paramodulation,[status(thm)],[f658,f23]) ).
fof(f675,plain,
! [X0,X1,X2] :
( less_equal(divide(divide(X0,X1),zero),X2)
| ~ quotient(divide(X0,zero),X1,X2) ),
inference(resolution,[status(thm)],[f226,f23]) ).
fof(f694,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[f672,f15]) ).
fof(f706,plain,
divide(a,idQa) = idQ_idQa,
inference(resolution,[status(thm)],[f694,f462]) ).
fof(f725,plain,
divide(idQ_idQa,a) = zero,
inference(paramodulation,[status(thm)],[f706,f112]) ).
fof(f978,plain,
less_equal(divide(idQa,divide(a,a)),divide(idQa,a)),
inference(resolution,[status(thm)],[f552,f23]) ).
fof(f1011,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[f675,f37]) ).
fof(f1022,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f1011,f48]) ).
fof(f1057,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(paramodulation,[status(thm)],[f1022,f23]) ).
fof(f1067,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f1057,f15]) ).
fof(f1089,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f1067,f48]) ).
fof(f1099,plain,
less_equal(divide(idQa,zero),divide(idQa,a)),
inference(backward_demodulation,[status(thm)],[f1089,f978]) ).
fof(f1144,plain,
! [X0] : quotient(X0,X0,zero),
inference(paramodulation,[status(thm)],[f1089,f23]) ).
fof(f1154,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[status(thm)],[f1144,f675]) ).
fof(f1290,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f1154,f48]) ).
fof(f1327,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(paramodulation,[status(thm)],[f1290,f23]) ).
fof(f1341,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f1327,f15]) ).
fof(f1392,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f1341,f48]) ).
fof(f1434,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(paramodulation,[status(thm)],[f1392,f23]) ).
fof(f1467,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f1434,f15]) ).
fof(f1493,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f1467,f47]) ).
fof(f1523,plain,
less_equal(idQa,divide(idQa,a)),
inference(backward_demodulation,[status(thm)],[f1493,f1099]) ).
fof(f1767,plain,
divide(idQa,a) = idQa,
inference(resolution,[status(thm)],[f1523,f579]) ).
fof(f1797,plain,
quotient(idQa,a,idQa),
inference(paramodulation,[status(thm)],[f1767,f23]) ).
fof(f1799,plain,
! [X0] :
( less_equal(divide(idQa,divide(idQ_idQa,a)),X0)
| ~ quotient(idQa_Q__idQ_idQa,a,X0) ),
inference(resolution,[status(thm)],[f1797,f310]) ).
fof(f1814,plain,
! [X0] :
( less_equal(divide(idQa,zero),X0)
| ~ quotient(idQa_Q__idQ_idQa,a,X0) ),
inference(forward_demodulation,[status(thm)],[f725,f1799]) ).
fof(f1815,plain,
! [X0] :
( less_equal(idQa,X0)
| ~ quotient(idQa_Q__idQ_idQa,a,X0) ),
inference(forward_demodulation,[status(thm)],[f1493,f1814]) ).
fof(f2005,plain,
less_equal(idQa,divide(idQa_Q__idQ_idQa,a)),
inference(resolution,[status(thm)],[f1815,f23]) ).
fof(f2022,plain,
divide(idQa_Q__idQ_idQa,a) = idQa,
inference(resolution,[status(thm)],[f2005,f579]) ).
fof(f2049,plain,
less_equal(idQa,idQa_Q__idQ_idQa),
inference(paramodulation,[status(thm)],[f2022,f36]) ).
fof(f2054,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2049,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:46:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 1.34/0.67 % Refutation found
% 1.34/0.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.34/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.34/0.68 % Elapsed time: 0.301864 seconds
% 1.34/0.68 % CPU time: 2.153122 seconds
% 1.34/0.68 % Total memory used: 64.311 MB
% 1.34/0.68 % Net memory used: 60.691 MB
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