%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 6.82s 6.28s
% Output : CNFRefutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 112 ( 112 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : ifeq(quotient(X,Y,zero),true,less_equal(X,Y),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : ifeq(quotient(X,Y,Z),true,less_equal(Z,X),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V3,V2,V4,V1,Z,V5,Y,X] : ifeq(quotient(V3,V2,V4),true,ifeq(quotient(V1,Z,V5),true,ifeq(quotient(Y,Z,V2),true,ifeq(quotient(X,Z,V3),true,ifeq(quotient(X,Y,V1),true,less_equal(V4,V5),true),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Y,X] : ifeq2(less_equal(Y,X),true,ifeq2(less_equal(X,Y),true,X,Y),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : quotient(X,X,zero) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] : quotient(X,zero,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Z,W2,Y,W1] : ifeq(quotient(X,Z,W2),true,ifeq(quotient(X,Y,W1),true,ifeq(less_equal(W1,Z),true,less_equal(W2,Y),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Z,Y,W1,X,W2] : ifeq(quotient(Z,Y,W1),true,ifeq(quotient(Z,X,W2),true,ifeq(less_equal(X,Y),true,less_equal(W1,W2),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,a,idQa) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
quotient(identity,idQa,idQ_idQa) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1] : ifeq(quotient(X0,X1,zero),true,less_equal(X0,X1),true) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1,X2] : ifeq(quotient(X0,X1,X2),true,less_equal(X2,X0),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,X4,X5),true,ifeq(quotient(X6,X4,X1),true,ifeq(quotient(X7,X4,X0),true,ifeq(quotient(X7,X6,X3),true,less_equal(X2,X5),true),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0,X1] : ifeq2(less_equal(X0,X1),true,ifeq2(less_equal(X1,X0),true,X1,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] : quotient(X0,X0,zero) = true,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
! [X0] : quotient(X0,zero,X0) = true,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4] : ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq(less_equal(X4,X1),true,less_equal(X2,X3),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4] : ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq(less_equal(X3,X1),true,less_equal(X2,X4),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
quotient(identity,a,idQa) = true,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f44,plain,
quotient(identity,idQa,idQ_idQa) = true,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f45,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) = true,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f65,plain,
! [X0] : ifeq(true,true,less_equal(X0,X0),true) = true,
inference(paramodulation,[status(thm)],[f37,f27]) ).
fof(f71,plain,
! [X0] : less_equal(X0,X0) = true,
inference(forward_demodulation,[status(thm)],[f25,f65]) ).
fof(f77,plain,
ifeq(true,true,less_equal(idQa_Q__idQ_idQa,idQa),true) = true,
inference(paramodulation,[status(thm)],[f45,f28]) ).
fof(f86,plain,
less_equal(idQa_Q__idQ_idQa,idQa) = true,
inference(forward_demodulation,[status(thm)],[f25,f77]) ).
fof(f175,plain,
! [X0,X1,X2,X3,X4] : ifeq(quotient(X0,X1,X2),true,ifeq(true,true,ifeq(quotient(X3,idQ_idQa,X1),true,ifeq(quotient(X4,idQ_idQa,X0),true,ifeq(quotient(X4,X3,idQa),true,less_equal(X2,idQa_Q__idQ_idQa),true),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f45,f29]) ).
fof(f213,plain,
! [X0,X1,X2,X3,X4] : ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,idQ_idQa,X1),true,ifeq(quotient(X4,idQ_idQa,X0),true,ifeq(quotient(X4,X3,idQa),true,less_equal(X2,idQa_Q__idQ_idQa),true),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f175]) ).
fof(f239,plain,
ifeq2(less_equal(idQa,idQa_Q__idQ_idQa),true,ifeq2(true,true,idQa_Q__idQ_idQa,idQa),idQa) = idQa,
inference(paramodulation,[status(thm)],[f86,f31]) ).
fof(f248,plain,
ifeq2(less_equal(idQa,idQa_Q__idQ_idQa),true,idQa_Q__idQ_idQa,idQa) = idQa,
inference(forward_demodulation,[status(thm)],[f24,f239]) ).
fof(f538,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(quotient(X0,idQ_idQa,zero),true,ifeq(quotient(X1,idQ_idQa,X2),true,ifeq(quotient(X1,X0,idQa),true,less_equal(X2,idQa_Q__idQ_idQa),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f38,f213]) ).
fof(f568,plain,
! [X0,X1,X2] : ifeq(quotient(X0,idQ_idQa,zero),true,ifeq(quotient(X1,idQ_idQa,X2),true,ifeq(quotient(X1,X0,idQa),true,less_equal(X2,idQa_Q__idQ_idQa),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f538]) ).
fof(f678,plain,
! [X0,X1,X2,X3] : ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X1),true,ifeq(true,true,less_equal(X2,X3),true),true),true) = true,
inference(paramodulation,[status(thm)],[f71,f40]) ).
fof(f714,plain,
! [X0,X1,X2,X3] : ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X1),true,less_equal(X2,X3),true),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f678]) ).
fof(f883,plain,
! [X0,X1] : ifeq(true,true,ifeq(quotient(identity,X0,X1),true,ifeq(less_equal(X0,a),true,less_equal(idQa,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f43,f41]) ).
fof(f914,plain,
! [X0,X1] : ifeq(quotient(identity,X0,X1),true,ifeq(less_equal(X0,a),true,less_equal(idQa,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f883]) ).
fof(f2352,plain,
! [X0] : ifeq(true,true,ifeq(quotient(identity,X0,idQa),true,less_equal(idQ_idQa,X0),true),true) = true,
inference(paramodulation,[status(thm)],[f44,f714]) ).
fof(f2371,plain,
! [X0] : ifeq(quotient(identity,idQ_idQa,X0),true,ifeq(true,true,less_equal(X0,idQa),true),true) = true,
inference(paramodulation,[status(thm)],[f44,f714]) ).
fof(f2392,plain,
! [X0] : ifeq(quotient(identity,X0,idQa),true,less_equal(idQ_idQa,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f2352]) ).
fof(f2403,plain,
! [X0] : ifeq(quotient(identity,idQ_idQa,X0),true,less_equal(X0,idQa),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f2371]) ).
fof(f2422,plain,
ifeq(true,true,less_equal(idQ_idQa,a),true) = true,
inference(paramodulation,[status(thm)],[f43,f2392]) ).
fof(f2430,plain,
less_equal(idQ_idQa,a) = true,
inference(forward_demodulation,[status(thm)],[f25,f2422]) ).
fof(f3380,plain,
ifeq(true,true,less_equal(divide(identity,idQ_idQa),idQa),true) = true,
inference(paramodulation,[status(thm)],[f33,f2403]) ).
fof(f3388,plain,
less_equal(divide(identity,idQ_idQa),idQa) = true,
inference(forward_demodulation,[status(thm)],[f25,f3380]) ).
fof(f3431,plain,
ifeq2(true,true,ifeq2(less_equal(idQa,divide(identity,idQ_idQa)),true,idQa,divide(identity,idQ_idQa)),divide(identity,idQ_idQa)) = divide(identity,idQ_idQa),
inference(paramodulation,[status(thm)],[f3388,f31]) ).
fof(f3472,plain,
ifeq2(less_equal(idQa,divide(identity,idQ_idQa)),true,idQa,divide(identity,idQ_idQa)) = divide(identity,idQ_idQa),
inference(forward_demodulation,[status(thm)],[f24,f3431]) ).
fof(f7173,plain,
! [X0] : ifeq(quotient(identity,idQ_idQa,X0),true,ifeq(true,true,less_equal(idQa,X0),true),true) = true,
inference(paramodulation,[status(thm)],[f2430,f914]) ).
fof(f7192,plain,
! [X0] : ifeq(quotient(identity,idQ_idQa,X0),true,less_equal(idQa,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f7173]) ).
fof(f7772,plain,
! [X0,X1] : ifeq(true,true,ifeq(quotient(X0,idQ_idQa,X1),true,ifeq(quotient(X0,idQ_idQa,idQa),true,less_equal(X1,idQa_Q__idQ_idQa),true),true),true) = true,
inference(paramodulation,[status(thm)],[f37,f568]) ).
fof(f7791,plain,
! [X0,X1] : ifeq(quotient(X0,idQ_idQa,X1),true,ifeq(quotient(X0,idQ_idQa,idQa),true,less_equal(X1,idQa_Q__idQ_idQa),true),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f7772]) ).
fof(f8075,plain,
ifeq(true,true,less_equal(idQa,divide(identity,idQ_idQa)),true) = true,
inference(paramodulation,[status(thm)],[f33,f7192]) ).
fof(f8094,plain,
ifeq2(true,true,idQa,divide(identity,idQ_idQa)) = divide(identity,idQ_idQa),
inference(backward_demodulation,[status(thm)],[f8096,f3472]) ).
fof(f8096,plain,
less_equal(idQa,divide(identity,idQ_idQa)) = true,
inference(forward_demodulation,[status(thm)],[f25,f8075]) ).
fof(f8145,plain,
idQa = divide(identity,idQ_idQa),
inference(forward_demodulation,[status(thm)],[f24,f8094]) ).
fof(f8154,plain,
quotient(identity,idQ_idQa,idQa) = true,
inference(paramodulation,[status(thm)],[f8145,f33]) ).
fof(f8176,plain,
! [X0] : ifeq(quotient(identity,idQ_idQa,X0),true,ifeq(true,true,less_equal(X0,idQa_Q__idQ_idQa),true),true) = true,
inference(paramodulation,[status(thm)],[f8154,f7791]) ).
fof(f8293,plain,
! [X0] : ifeq(quotient(identity,idQ_idQa,X0),true,less_equal(X0,idQa_Q__idQ_idQa),true) = true,
inference(forward_demodulation,[status(thm)],[f25,f8176]) ).
fof(f8477,plain,
ifeq(true,true,less_equal(idQa,idQa_Q__idQ_idQa),true) = true,
inference(paramodulation,[status(thm)],[f8154,f8293]) ).
fof(f8504,plain,
ifeq2(true,true,idQa_Q__idQ_idQa,idQa) = idQa,
inference(backward_demodulation,[status(thm)],[f8513,f248]) ).
fof(f8513,plain,
less_equal(idQa,idQa_Q__idQ_idQa) = true,
inference(forward_demodulation,[status(thm)],[f25,f8477]) ).
fof(f8542,plain,
idQa_Q__idQ_idQa = idQa,
inference(forward_demodulation,[status(thm)],[f24,f8504]) ).
fof(f8543,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8542,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n018.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 20 20:48:33 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 6.82/6.28 % Refutation found
% 6.82/6.28 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.82/6.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.56/6.35 % Elapsed time: 0.968577 seconds
% 5.56/6.35 % CPU time: 7.528077 seconds
% 5.56/6.35 % Total memory used: 230.157 MB
% 5.56/6.35 % Net memory used: 227.198 MB
%------------------------------------------------------------------------------