TSTP Solution File: HEN009-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:21:47 EDT 2024
% Result : Unsatisfiable 2.17s 0.69s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 137 ( 61 unt; 0 def)
% Number of atoms : 269 ( 38 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 261 ( 129 ~; 128 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 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] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
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] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| 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] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| Z = W ),
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(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f16,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [V4,V5] :
( ! [V1,Z] :
( ! [V2,V3] :
( ! [X] :
( ! [Y] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2) )
| ~ quotient(X,Z,V3) )
| ~ quotient(V3,V2,V4) )
| ~ quotient(V1,Z,V5) )
| less_equal(V4,V5) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0] : less_equal(X0,identity),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f23,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f24,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f27,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
idQa != idQ__idQ_idQa,
inference(cnf_transformation,[status(esa)],[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(f43,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f21,f37]) ).
fof(f44,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(a,X0,X1)
| ~ quotient(identity,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(idQa,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f19,f26]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(idQ_idQa,X0,X1)
| ~ quotient(identity,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(idQ__idQ_idQa,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f19,f28]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(divide(X3,X0),X1,X6)
| less_equal(X5,X6) ),
inference(resolution,[status(thm)],[f19,f23]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ quotient(identity,X0,X1)
| ~ quotient(X1,divide(idQ_idQa,X0),X2)
| ~ quotient(idQ__idQ_idQa,X0,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f51,f23]) ).
fof(f61,plain,
! [X0] :
( ~ quotient(identity,idQa,X0)
| idQ_idQa = X0 ),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f64,plain,
! [X0,X1] :
( ~ quotient(X0,identity,X1)
| zero = X1 ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f67,plain,
! [X0] : zero = divide(X0,identity),
inference(resolution,[status(thm)],[f64,f23]) ).
fof(f71,plain,
idQ_idQa = divide(identity,idQa),
inference(resolution,[status(thm)],[f61,f23]) ).
fof(f83,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f65,f38]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ~ quotient(identity,X0,X1)
| ~ quotient(X1,divide(a,X0),X2)
| ~ quotient(idQa,X0,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f50,f23]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X2,zero,X3)
| ~ quotient(divide(X0,zero),X1,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f53,f30]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,idQa,X1)
| ~ quotient(X1,idQ_idQa,X2)
| ~ quotient(divide(X0,identity),idQa,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f53,f27]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,idQa,X1)
| ~ quotient(X1,idQ_idQa,X2)
| ~ quotient(zero,idQa,X3)
| less_equal(X2,X3) ),
inference(forward_demodulation,[status(thm)],[f67,f111]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,a,X1)
| ~ quotient(X1,idQa,X2)
| ~ quotient(divide(X0,identity),a,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f53,f26]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,a,X1)
| ~ quotient(X1,idQa,X2)
| ~ quotient(zero,a,X3)
| less_equal(X2,X3) ),
inference(forward_demodulation,[status(thm)],[f67,f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,idQ_idQa,X1)
| ~ quotient(X1,idQ__idQ_idQa,X2)
| ~ quotient(divide(X0,identity),idQ_idQa,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,idQ_idQa,X1)
| ~ quotient(X1,idQ__idQ_idQa,X2)
| ~ quotient(zero,idQ_idQa,X3)
| less_equal(X2,X3) ),
inference(forward_demodulation,[status(thm)],[f67,f115]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X2,divide(X3,X1),X4)
| ~ quotient(divide(X0,X3),X1,X5)
| less_equal(X4,X5) ),
inference(resolution,[status(thm)],[f53,f23]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ quotient(divide(X0,idQ_idQa),idQ__idQ_idQa,X1)
| ~ quotient(zero,idQ_idQa,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f116,f23]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ quotient(identity,X0,X1)
| ~ quotient(idQ__idQ_idQa,X0,X2)
| less_equal(divide(X1,divide(idQ_idQa,X0)),X2) ),
inference(resolution,[status(thm)],[f55,f23]) ).
fof(f181,plain,
! [X0,X1] :
( ~ quotient(zero,idQ_idQa,X0)
| less_equal(divide(divide(X1,idQ_idQa),idQ__idQ_idQa),X0) ),
inference(resolution,[status(thm)],[f122,f23]) ).
fof(f232,plain,
! [X0] : less_equal(divide(divide(X0,idQ_idQa),idQ__idQ_idQa),zero),
inference(resolution,[status(thm)],[f181,f30]) ).
fof(f235,plain,
! [X0] : zero = divide(divide(X0,idQ_idQa),idQ__idQ_idQa),
inference(resolution,[status(thm)],[f232,f44]) ).
fof(f257,plain,
! [X0] : quotient(divide(X0,idQ_idQa),idQ__idQ_idQa,zero),
inference(paramodulation,[status(thm)],[f235,f23]) ).
fof(f259,plain,
! [X0] : less_equal(divide(X0,idQ_idQa),idQ__idQ_idQa),
inference(resolution,[status(thm)],[f257,f15]) ).
fof(f268,plain,
! [X0] :
( ~ less_equal(idQ__idQ_idQa,divide(X0,idQ_idQa))
| divide(X0,idQ_idQa) = idQ__idQ_idQa ),
inference(resolution,[status(thm)],[f259,f21]) ).
fof(f312,plain,
! [X0] :
( ~ quotient(idQ__idQ_idQa,a,X0)
| less_equal(divide(idQa,divide(idQ_idQa,a)),X0) ),
inference(resolution,[status(thm)],[f178,f26]) ).
fof(f327,plain,
less_equal(divide(idQa,divide(idQ_idQa,a)),divide(idQ__idQ_idQa,a)),
inference(resolution,[status(thm)],[f312,f23]) ).
fof(f337,plain,
quotient(divide(idQa,divide(idQ_idQa,a)),divide(idQ__idQ_idQa,a),zero),
inference(resolution,[status(thm)],[f327,f14]) ).
fof(f497,plain,
! [X0,X1,X2] :
( ~ quotient(identity,X0,X1)
| ~ quotient(idQa,X0,X2)
| less_equal(divide(X1,divide(a,X0)),X2) ),
inference(resolution,[status(thm)],[f108,f23]) ).
fof(f790,plain,
! [X0,X1] :
( ~ quotient(idQ_idQa,idQ_idQa,X0)
| ~ quotient(zero,idQa,X1)
| less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f112,f27]) ).
fof(f791,plain,
! [X0,X1,X2] :
( ~ quotient(divide(X0,idQa),idQ_idQa,X1)
| ~ quotient(zero,idQa,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f112,f23]) ).
fof(f795,plain,
! [X0] :
( ~ quotient(zero,idQa,X0)
| less_equal(divide(idQ_idQa,idQ_idQa),X0) ),
inference(resolution,[status(thm)],[f790,f23]) ).
fof(f811,plain,
! [X0,X1,X2,X3] :
( ~ quotient(divide(X0,X1),zero,X2)
| ~ quotient(divide(X0,zero),X1,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f110,f23]) ).
fof(f814,plain,
! [X0,X1] :
( ~ quotient(idQa,idQa,X0)
| ~ quotient(zero,a,X1)
| less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f114,f26]) ).
fof(f815,plain,
! [X0,X1,X2] :
( ~ quotient(divide(X0,a),idQa,X1)
| ~ quotient(zero,a,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f114,f23]) ).
fof(f940,plain,
less_equal(divide(idQ_idQa,idQ_idQa),zero),
inference(resolution,[status(thm)],[f795,f30]) ).
fof(f943,plain,
zero = divide(idQ_idQa,idQ_idQa),
inference(resolution,[status(thm)],[f940,f44]) ).
fof(f1049,plain,
! [X0,X1,X2] :
( ~ quotient(idQ__idQ_idQa,divide(X0,idQ_idQa),X1)
| ~ quotient(divide(identity,X0),idQ_idQa,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f118,f28]) ).
fof(f1115,plain,
! [X0,X1] :
( ~ quotient(divide(identity,X0),idQ_idQa,X1)
| less_equal(divide(idQ__idQ_idQa,divide(X0,idQ_idQa)),X1) ),
inference(resolution,[status(thm)],[f1049,f23]) ).
fof(f1124,plain,
! [X0] : less_equal(divide(idQ__idQ_idQa,divide(X0,idQ_idQa)),divide(divide(identity,X0),idQ_idQa)),
inference(resolution,[status(thm)],[f1115,f23]) ).
fof(f1145,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),divide(idQ_idQa,idQ_idQa)),
inference(paramodulation,[status(thm)],[f71,f1124]) ).
fof(f1146,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(forward_demodulation,[status(thm)],[f943,f1145]) ).
fof(f1151,plain,
zero = divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolution,[status(thm)],[f1146,f44]) ).
fof(f1190,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(paramodulation,[status(thm)],[f1151,f23]) ).
fof(f1206,plain,
less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolution,[status(thm)],[f1190,f15]) ).
fof(f1219,plain,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(resolution,[status(thm)],[f1206,f268]) ).
fof(f1248,plain,
( spl0_77
<=> less_equal(idQa,idQ__idQ_idQa) ),
introduced(split_symbol_definition) ).
fof(f1250,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| spl0_77 ),
inference(component_clause,[status(thm)],[f1248]) ).
fof(f1251,plain,
( spl0_78
<=> divide(idQa,idQ_idQa) = idQa ),
introduced(split_symbol_definition) ).
fof(f1252,plain,
( divide(idQa,idQ_idQa) = idQa
| ~ spl0_78 ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1254,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| divide(idQa,idQ_idQa) = idQa ),
inference(paramodulation,[status(thm)],[f1219,f43]) ).
fof(f1255,plain,
( ~ spl0_77
| spl0_78 ),
inference(split_clause,[status(thm)],[f1254,f1248,f1251]) ).
fof(f1479,plain,
! [X0] :
( ~ quotient(zero,a,X0)
| less_equal(divide(idQa,idQa),X0) ),
inference(resolution,[status(thm)],[f814,f23]) ).
fof(f1480,plain,
less_equal(divide(idQa,idQa),zero),
inference(resolution,[status(thm)],[f1479,f30]) ).
fof(f1483,plain,
zero = divide(idQa,idQa),
inference(resolution,[status(thm)],[f1480,f44]) ).
fof(f1510,plain,
quotient(idQa,idQa,zero),
inference(paramodulation,[status(thm)],[f1483,f23]) ).
fof(f1790,plain,
! [X0,X1] :
( ~ quotient(zero,idQa,X0)
| less_equal(divide(divide(X1,idQa),idQ_idQa),X0) ),
inference(resolution,[status(thm)],[f791,f23]) ).
fof(f1954,plain,
! [X0] : less_equal(divide(divide(X0,idQa),idQ_idQa),zero),
inference(resolution,[status(thm)],[f1790,f30]) ).
fof(f1957,plain,
! [X0] : zero = divide(divide(X0,idQa),idQ_idQa),
inference(resolution,[status(thm)],[f1954,f44]) ).
fof(f2016,plain,
! [X0] : quotient(divide(X0,idQa),idQ_idQa,zero),
inference(paramodulation,[status(thm)],[f1957,f23]) ).
fof(f2022,plain,
! [X0] : less_equal(divide(X0,idQa),idQ_idQa),
inference(resolution,[status(thm)],[f2016,f15]) ).
fof(f2042,plain,
! [X0] :
( ~ less_equal(idQ_idQa,divide(X0,idQa))
| divide(X0,idQa) = idQ_idQa ),
inference(resolution,[status(thm)],[f2022,f21]) ).
fof(f2096,plain,
! [X0] :
( ~ quotient(idQa,idQa,X0)
| less_equal(divide(idQ_idQa,divide(a,idQa)),X0) ),
inference(resolution,[status(thm)],[f497,f27]) ).
fof(f2324,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(resolution,[status(thm)],[f2096,f1510]) ).
fof(f2327,plain,
zero = divide(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[f2324,f44]) ).
fof(f2367,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(paramodulation,[status(thm)],[f2327,f23]) ).
fof(f2379,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[f2367,f15]) ).
fof(f2391,plain,
divide(a,idQa) = idQ_idQa,
inference(resolution,[status(thm)],[f2379,f2042]) ).
fof(f2427,plain,
divide(idQ_idQa,a) = zero,
inference(paramodulation,[status(thm)],[f2391,f83]) ).
fof(f2440,plain,
! [X0,X1,X2] :
( ~ quotient(divide(X0,zero),X1,X2)
| less_equal(divide(divide(X0,X1),zero),X2) ),
inference(resolution,[status(thm)],[f811,f23]) ).
fof(f2599,plain,
quotient(divide(idQa,zero),divide(idQ__idQ_idQa,a),zero),
inference(backward_demodulation,[status(thm)],[f2427,f337]) ).
fof(f2713,plain,
! [X0,X1] :
( ~ quotient(zero,a,X0)
| less_equal(divide(divide(X1,a),idQa),X0) ),
inference(resolution,[status(thm)],[f815,f23]) ).
fof(f2885,plain,
! [X0] : less_equal(divide(divide(X0,a),idQa),zero),
inference(resolution,[status(thm)],[f2713,f30]) ).
fof(f2888,plain,
! [X0] : zero = divide(divide(X0,a),idQa),
inference(resolution,[status(thm)],[f2885,f44]) ).
fof(f2934,plain,
! [X0] : quotient(divide(X0,a),idQa,zero),
inference(paramodulation,[status(thm)],[f2888,f23]) ).
fof(f3190,plain,
! [X0] : less_equal(divide(X0,a),idQa),
inference(resolution,[status(thm)],[f2934,f15]) ).
fof(f3208,plain,
! [X0] :
( ~ less_equal(idQa,divide(X0,a))
| divide(X0,a) = idQa ),
inference(resolution,[status(thm)],[f3190,f21]) ).
fof(f3652,plain,
less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero),
inference(resolution,[status(thm)],[f2440,f2599]) ).
fof(f4069,plain,
zero = divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(resolution,[status(thm)],[f3652,f44]) ).
fof(f4096,plain,
( spl0_182
<=> less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero) ),
introduced(split_symbol_definition) ).
fof(f4098,plain,
( ~ less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero)
| spl0_182 ),
inference(component_clause,[status(thm)],[f4096]) ).
fof(f4099,plain,
( spl0_183
<=> divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero) = divide(idQa,divide(idQ__idQ_idQa,a)) ),
introduced(split_symbol_definition) ).
fof(f4100,plain,
( divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero) = divide(idQa,divide(idQ__idQ_idQa,a))
| ~ spl0_183 ),
inference(component_clause,[status(thm)],[f4099]) ).
fof(f4102,plain,
( ~ less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero)
| divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero) = divide(idQa,divide(idQ__idQ_idQa,a)) ),
inference(paramodulation,[status(thm)],[f4069,f43]) ).
fof(f4103,plain,
( ~ spl0_182
| spl0_183 ),
inference(split_clause,[status(thm)],[f4102,f4096,f4099]) ).
fof(f4108,plain,
quotient(divide(idQa,divide(idQ__idQ_idQa,a)),zero,zero),
inference(paramodulation,[status(thm)],[f4069,f23]) ).
fof(f4111,plain,
less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(resolution,[status(thm)],[f4108,f15]) ).
fof(f4112,plain,
( $false
| spl0_182 ),
inference(forward_subsumption_resolution,[status(thm)],[f4111,f4098]) ).
fof(f4113,plain,
spl0_182,
inference(contradiction_clause,[status(thm)],[f4112]) ).
fof(f4128,plain,
( zero = divide(idQa,divide(idQ__idQ_idQa,a))
| ~ spl0_183 ),
inference(forward_demodulation,[status(thm)],[f4069,f4100]) ).
fof(f4221,plain,
( quotient(idQa,divide(idQ__idQ_idQa,a),zero)
| ~ spl0_183 ),
inference(paramodulation,[status(thm)],[f4128,f23]) ).
fof(f4234,plain,
( less_equal(idQa,divide(idQ__idQ_idQa,a))
| ~ spl0_183 ),
inference(resolution,[status(thm)],[f4221,f15]) ).
fof(f4246,plain,
( divide(idQ__idQ_idQa,a) = idQa
| ~ spl0_183 ),
inference(resolution,[status(thm)],[f4234,f3208]) ).
fof(f4328,plain,
( less_equal(idQa,idQ__idQ_idQa)
| ~ spl0_183 ),
inference(paramodulation,[status(thm)],[f4246,f37]) ).
fof(f4329,plain,
( $false
| spl0_77
| ~ spl0_183 ),
inference(forward_subsumption_resolution,[status(thm)],[f4328,f1250]) ).
fof(f4330,plain,
( spl0_77
| ~ spl0_183 ),
inference(contradiction_clause,[status(thm)],[f4329]) ).
fof(f4338,plain,
( idQ__idQ_idQa = idQa
| ~ spl0_78 ),
inference(forward_demodulation,[status(thm)],[f1219,f1252]) ).
fof(f4339,plain,
( $false
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[status(thm)],[f4338,f29]) ).
fof(f4340,plain,
~ spl0_78,
inference(contradiction_clause,[status(thm)],[f4339]) ).
fof(f4341,plain,
$false,
inference(sat_refutation,[status(thm)],[f1255,f4103,f4113,f4330,f4340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 20:45:25 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 2.17/0.69 % Refutation found
% 2.17/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.17/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.39/0.71 % Elapsed time: 0.362294 seconds
% 2.39/0.71 % CPU time: 2.405728 seconds
% 2.39/0.71 % Total memory used: 48.588 MB
% 2.39/0.71 % Net memory used: 46.085 MB
%------------------------------------------------------------------------------